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<title>Bit Operations</title>
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Bit Operations</h4>
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This chapter covers operations on bits, the smallest data units. Bit operations
are among the most fundamental features of microprocessors.</p>
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System programmers must understand bit operations at least to use<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">flag</i>parameters
correctly.</p>
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Representation of data at the lowest level</h5>
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Programming languages are abstractions. A user type like<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">Student</code>defined
in a programming language is not directly related to the internals of the
computer. Programming languages are tools that help humans use the hardware
without needing to know the details of the hardware.</p>
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Although it is usually not necessary to deal with the hardware directly, it is
helpful to understand how data is represented at hardware level.</p>
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Transistor</h6>
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The processing abilities of modern electronic devices are mostly based on the
electronic element called<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">the
transistor</i>. A significant ability of the transistor is that it can be
controlled by other parts of the electronic circuit that the transistor is a
part of. In a way, it allows the electronic circuit be aware of itself and be
able to change its own state.</p>
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Bit</h6>
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The smallest unit of information is a bit. A bit can be represented by any
two-state system (e.g. by a special arrangement of a few transistors of an
electronic circuit). A bit can have one of two values: 0 or 1. In the computer's
memory, the information that is stored in a bit persists until a new value is
stored or until the energy source is disconnected.</p>
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Computers do not provide direct access to bits. One reason is that doing so
would complicate the design of the computer and as a consequence make the
computer more expensive. Another reason is that there are not many concepts that
can be represented by a single bit.</p>
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Byte</h6>
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A byte is a combination of 8 bits. The smallest unit of information that can be
addressed uniquely is a byte. Computers read from or write to memory at least
one byte at a time.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
For that reason, although it carries one bit of information (<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">false</code><span class="Apple-converted-space"> </span>or<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">true</code>),
even<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">bool</code><span class="Apple-converted-space"> </span>must
be implemented as one byte:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> writefln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"%s is %s byte(s)"</span>, <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">bool</span>.stringof, <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">bool</span>.sizeof);
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<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">bool is 1 byte(s)
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Register</h6>
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Data that are being operated on in a microprocessor are stored in registers.
Registers provide very limited but very fast operations.</p>
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The size of the registers depend on the architecture of the microprocessor. For
example, 32-bit microprocessors commonly have 4-byte registers and 64-bit
microprocessors commonly have 8-byte registers. The size of the registers
determine how much information the microprocessor can process efficiently at a
time and how many memory addresses that it can support.</p>
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Every task that is achieved by a programming language ends up being executed by
one or more registers of the microprocessor.</p>
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Binary number system</h5>
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The decimal number system which is used in daily life consists of 10 numerals:
0123456789. In contrast, the binary number system which is used by computer
hardware consists of 2 numerals: 0 and 1. This is a direct consequence of a bit
consisting of two values. If bits had three values then the computers would use
a number system based on three numerals.</p>
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The digits of the decimal system are named incrementally as<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">ones</i>,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">tens</i>,<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">hundreds</i>,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">thousands</i>,
etc. For example, the number 1023 can be expanded as in the following way:</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">1023 == 1 count of thousand, no hundred, 2 counts of ten, and 3 counts of one
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Naturally, moving one digit to the left multiplies the value of that digit by
10: 1, 10, 100, 1000, etc.</p>
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When the same rules are applied to a system that has two numerals, we arrive at
the binary number system. The digits are named incrementally as<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">ones</i>,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">twos</i>,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">fours</i>,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">eights</i>,
etc. In other words, moving one digit to the left would multiply the value of
that digit by 2: 1, 2, 4, 8, etc. For example, the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">binary</i><span class="Apple-converted-space"> </span>number
1011 can be expanded as in the following way:</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">1011 == 1 count of eight, no four, 1 count of two, and 1 count of one
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To make it easy to refer to digits, they are numbered from the rightmost digit
to the leftmost digit, starting by 0. The following table lists the values of
all of the digits of a 32-bit unsigned number in the binary system:</p>
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Digit</th>
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Value</th>
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<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
31</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2,147,483,648</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
30</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1,073,741,824</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
29</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
536,870,912</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
28</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
268,435,456</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
27</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
134,217,728</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
26</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
67,108,864</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
25</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
33,554,432</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
24</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16,777,216</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
23</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
8,388,608</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
22</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4,194,304</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
21</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2,097,152</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
20</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1,048,576</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
19</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
524,288</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
18</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
262,144</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
17</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
131,072</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
16</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
65,536</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
15</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
32,768</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
14</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16,384</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
13</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
8,192</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
12</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4,096</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
11</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2,048</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
10</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1,024</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
9</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
512</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
8</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
256</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
7</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
128</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
6</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
64</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
5</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
32</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
4</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
3</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
8</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
2</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1</td>
</tr>
</table>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The bits that have higher values are called the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">upper</i><span class="Apple-converted-space"> </span>bits
and the bits that have lower values are called the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">lower</i><span class="Apple-converted-space"> </span>bits.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Remembering from<span class="Apple-converted-space"> </span><a href="http://ddili.org/ders/d.en/literals.html" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: purple; text-decoration: none; background-position: initial initial; background-repeat: initial initial;">the
Literals chapter</a><span class="Apple-converted-space"> </span>that binary
literals are specified by the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">0b</code><span class="Apple-converted-space"> </span>prefix,
the following program demonstrates how the value of a literal would correspond
to the rows of the previous table:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// 1073741824 4 1
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ↓ ↓ ↓
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number = 0b_01000000_00000000_00000000_00000101;
writeln(number);
}
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The output:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">1073741829
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Note that the literal consists of only three non-zero bits. The value that is
printed is the sum of the values that correspond to those bits from the previous
table: 1073741824 + 4 + 1 == 1073741829.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 18px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">sign</i><span class="Apple-converted-space"> </span>bit
of signed integer types</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The uppermost bit of a signed type determines whether the value is positive or
negative:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> number = 0b_<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">1</span>0000000_00000000_00000000_00000000;
writeln(number);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">-2147483648
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
However, the uppermost bit is not entirely separate from the value. For example,
as evidenced above, the fact that all of the other bits of the number being 0
does not mean that the value is -0. (In fact, -0 is not a valid value for
integers.) I will not get into more detail in this chapter other than noting
that this is due to the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">twos
complement</i>representation, which is used by D as well.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
What is important here is that 2,147,483,648; the highest value in the previous
table, is only for unsigned integer types. The same experiment with<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code><span class="Apple-converted-space"> </span>would
print that exact value:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span></span> number = 0b_10000000_00000000_00000000_00000000;
writeln(number);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">2147483648
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Partly for that reason, unless there is a reason not to, bit operations must
always be executed on unsigned types:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">ubyte</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code>,
and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">ulong</code>.</p>
<h5 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.25em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Hexadecimal number system</h5>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As can be seen in the literals above, consisting only of 0s and 1s, the binary
system may not be readable especially when the numbers are large.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
For that reason, the more readable hexadecimal system has been widely adopted
especially in computer technologies.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The hexadecimal system has 16 numerals. Since alphabets do not have more than 10
numerals, this system borrows 6 letters from the Latin alphabet and uses them
along with regular numerals: 0123456789abcdef. The numerals a, b, c, d, e, and f
have the values 10, 11, 12, 13, 14, and 15, respectively. The letters ABCDEF can
be used as well.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Similar to other number systems, the value of every digit is 16 times the value
of the digit on its right-hand side: 1, 16, 256, 4096, etc. For example, the
values of all of the digits of an 8-digit unsigned hexadecimal number are the
following:</p>
<table border="1" cellpadding="4" cellspacing="0" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;" width="250">
<tbody style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tr style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Digit</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Value</th>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
7</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
268,435,456</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
6</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16,777,216</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
5</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1,048,576</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
4</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
65,536</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
3</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4,096</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
2</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
256</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
16</td>
</tr>
<tr align="right" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1</td>
</tr>
</table>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Remembering that hexadecimal literals are specified by the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">0x</code><span class="Apple-converted-space"> </span>prefix,
we can see how the values of the digits contribute to the overall value of a
number:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// 1048576 4096 1
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ↓ ↓ ↓
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> sayı = 0x_0030_a00f;
writeln(sayı);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">3186703
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The value that is printed is by the contributions of all of the non-zero digits:
3 count of 1048576,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">a</code><span class="Apple-converted-space"> </span>count
of 4096, and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">f</code><span class="Apple-converted-space"> </span>count
of 1. Remembering that<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">a</code><span class="Apple-converted-space"> </span>represents
10 and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">f</code><span class="Apple-converted-space"> </span>represents
15, the value is 3145728 + 40960 + 15 == 3186703.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
It is straightforward to convert between binary and hexadecimal numbers. In
order to convert a hexadecimal number to binary, the digits of the hexadecimal
number are converted to their binary representations individually. The
corresponding representations in the three number systems are as in the
following table:</p>
<table border="1" cellpadding="4" cellspacing="0" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;" width="250">
<tbody style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tr style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<th align="center" scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Hexadecimal</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Binary</th>
<th scope="col" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
Decimal</th>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0000</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
0</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0001</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
1</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
2</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0010</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
2</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
3</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0011</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
3</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
4</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0100</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
4</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
5</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0101</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
5</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
6</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0110</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
6</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
7</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
0111</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
7</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
8</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1000</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
8</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
9</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1001</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
9</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
a</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1010</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
10</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
b</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1011</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
11</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
c</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1100</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
12</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
d</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1101</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
13</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
e</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1110</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
14</td>
</tr>
<tr align="center" style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
f</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
<tt style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
1111</tt></td>
<td style="margin: 1em; padding: 0px; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; font-family: monospace; background-position: initial initial; background-repeat: initial initial;">
15</td>
</tr>
</table>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
For example, the hexadecimal number 0x0030a00f can be written in the binary form
by converting its digits individually according to the previous table:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// hexadecimal: 0 0 3 0 a 0 0 f
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> binary = 0b_0000_0000_0011_0000_1010_0000_0000_1111;
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Converting from binary to hexadecimal is the reverse: The digits of the binary
number are converted to their hexadecimal representations four digits at a time.
For example, here is how to write in hexadecimal the same binary value that we
have used earlier:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// binary: 0100 0000 0000 0000 0000 0000 0000 0101
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> hexadecimal = 0x___4____0____0____0____0____0____0____5;
</pre>
<h5 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.25em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Bit operations</h5>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
After going over how values are represented by bits and how numbers are
represented in binary and hexadecimal, we can now see operations that change
values at bit-level.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Because there is no direct access to individual bits, even though these
operations are at bit-level, they affect at least 8 bits at a time. For example,
for a variable of type<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">ubyte</code>,
a bit operation would be applied to all of the 8 bits of that variable.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As the uppermost bit is the sign bit for signed types, I will ignore signed
types and use only<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">uint</code><span class="Apple-converted-space"> </span>in
the examples below. You can repeat these operations with<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">ulong</code><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">ubyte</code>,
as well as<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">byte</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">int</code>,
and<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">long</code><span class="Apple-converted-space"> </span>as
long as you remember the special meaning of the uppermost bit.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Let's first define a function which will be useful later when examining how bit
operators work. This function will print a value in binary, hexadecimal, and
decimal systems:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">import</span> std.stdio;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> print(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> number)
{
writefln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"%032b %08x %10s"</span>, number, number, number);
}
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">void</span> main()
{
print(123456789);
}
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Here is the same value printed in the binary, hexadecimal, and decimal number
systems:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">00000111010110111100110100010101 075bcd15 123456789
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Complement operator:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">~</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Not be confused with the<span class="Apple-converted-space"> </span>binary<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">~</code><span class="Apple-converted-space"> </span>operator
that is used for array concatenation, this is the unary<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">~</code><span class="Apple-converted-space"> </span>operator.</i></p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator converts each bit of a value to its opposite: The bits that are 0
become 1, and the bits that are 1 become 0.</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 123456789;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(value);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"~ --------------------------------"</span>);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">~</span>value);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The effect is obvious in the binary representation. Every bit has been reversed
(under the dashed line):</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> 00000111010110111100110100010101 075bcd15 123456789
~ --------------------------------
11111000101001000011001011101010 f8a432ea 4171510506
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Here is the summary of how the unary<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">~</code><span class="Apple-converted-space"> </span>operator
works:</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">~0 → 1
~1 → 0
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 18px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
And</i><span class="Apple-converted-space"> </span>operator:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
&</code><span class="Apple-converted-space"> </span>is a binary operator,
written between two expressions. The microprocessor considers two corresponding
bits of the two expressions separately from all of the other bits: Bits 31, 30,
29, etc. of the expressions are evaluated separately. The value of each
resultant bit is 1 if both of the corresponding bits of the expressions are 1; 0
otherwise.</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> lhs = 123456789;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> rhs = 987654321;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(rhs);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"& --------------------------------"</span>);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">&</span> rhs);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The following output contains first the left-hand side expression (lhs) and then
the right-hand side expression (rhs). The result of the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&</code>operation
is under the dashed line:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> 00000111010110111100110100010101 075bcd15 123456789
00111010110111100110100010110001 3ade68b1 987654321
& --------------------------------
00000010010110100100100000010001 025a4811 39471121
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Note that the bits of the result that have the value 1 are the ones where the
corresponding bits of the expressions are both 1.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator is called the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">and</i><span class="Apple-converted-space"> </span>operator
because it produces 1 when both the left-hand side<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">and</i><span class="Apple-converted-space"> </span>the
right-hand side bits are 1. Among the four possible combinations of 0 and 1
values, only the one where both of the values are 1 produces 1:</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">0 & 0 → 0
0 & 1 → 0
1 & 0 → 0
1 & 1 → 1
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Observations:</p>
<ul style="margin: 0.5em 1em 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
When one of the bits is 0, regardless of the other bit the result is always
0. Accordingly, "<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">anding</i><span class="Apple-converted-space"> </span>a
bit by 0" means to clear that bit.</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
When one of the bits is 1, the result is the value of the other bit;<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">anding</i><span class="Apple-converted-space"> </span>by
1 has no effect.</li>
</ul>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 18px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Or</i><span class="Apple-converted-space"> </span>operator:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">|</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
|</code><span class="Apple-converted-space"> </span>is a binary operator,
written between two expressions. The microprocessor considers two corresponding
bits of the two expressions separately from all of the other bits. The value of
each resultant bit is 0 if both of the corresponding bits of the expressions are
0; 1 otherwise.</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> lhs = 123456789;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> rhs = 987654321;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(rhs);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"| --------------------------------"</span>);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">|</span> rhs);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> 00000111010110111100110100010101 075bcd15 123456789
00111010110111100110100010110001 3ade68b1 987654321
| --------------------------------
00111111110111111110110110110101 3fdfedb5 1071639989
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Note that the bits of the result that have the value 0 are the ones where the
corresponding bits of the expressions are both 0. When the corresponding bit in
the left-hand side or in the right-hand side is 1, then the result is 1:</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">0 | 0 → 0
0 | 1 → 1
1 | 0 → 1
1 | 1 → 1
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Observations:</p>
<ul style="margin: 0.5em 1em 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
When one of the bits is 1, regardless of the other bit the result is always
1. Accordingly, "<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">orring</i><span class="Apple-converted-space"> </span>a
bit by 1" means to set it.</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
When one of the bits is 0, the result is the value of the other bit;<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">orring</i><span class="Apple-converted-space"> </span>by
0 has no effect.</li>
</ul>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 18px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Xor</i><span class="Apple-converted-space"> </span>operator:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">^</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Xor</i><span class="Apple-converted-space"> </span>is the short for<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">exclusive
or</i>. This is a binary operator as well. It produces 1 if the corresponding
bits of the two expressions are different:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> lhs = 123456789;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> rhs = 987654321;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(rhs);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"^ --------------------------------"</span>);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">^</span> rhs);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> 00000111010110111100110100010101 075bcd15 123456789
00111010110111100110100010110001 3ade68b1 987654321
^ --------------------------------
00111101100001011010010110100100 3d85a5a4 1032168868
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Note that the bits of the result that have the value 1 are the ones where the
corresponding bits of the expressions are different from each other.</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">0 ^ 0 → 0
0 ^ 1 → 1
1 ^ 0 → 1
1 ^ 1 → 0
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Observation:</p>
<ul style="margin: 0.5em 1em 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
"<i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">Xorring</i><span class="Apple-converted-space"> </span>a
bit" with itself means to clear that bit.</li>
</ul>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Regardless of its value,<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">xorring</i><span class="Apple-converted-space"> </span>a
variable with itself always produces 0:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 123456789;
print(value ^ value);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">00000000000000000000000000000000 00000000 0
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Right-shift operator:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">>></code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator shifts the bits of an expression by the specified number of bits
to the right. The rightmost bits, which do not have room to shift into, get<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">dropped</i><span class="Apple-converted-space"> </span>from
the value. For unsigned types, the leftmost bits are filled with zeros.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The following example produces a result by shifting a value by two bits to the
right:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 123456789;
print(value);
print(value <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">>></span> 2);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
In the following output, I have indicated the bits that are going to be lost due
to dropping off from the right-hand side in gray, and the leftmost bits that get
the value 0 in blue:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">000001110101101111001101000101<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: gray; background-position: initial initial; background-repeat: initial initial;">01</span> 075bcd15 123456789
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">00</span>000001110101101111001101000101 01d6f345 30864197
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Note that the bits other than gray and blue have been shifted two bit positions
to the right.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The new bits that enter from the left-hand side are 0 only for unsigned types.
For signed types, the value of the leftmost bits are determined by a process
called<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">sign
extension</i>. Sign extension preserves the value of the sign bit of the
original expression. The value of that bit is used for all of the bits that<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">enter</i><span class="Apple-converted-space"> </span>from
the left.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Let's see this effect on a value of a signed type where the sign bit is 1 (i.e.
the value is negative):</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span></span> value = 0x80010300;
print(value);
print(value >> 3);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Because the leftmost bit of the original value is 1, all of the new bits of the
result are 1 as well:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><u style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">1</u>0000000000000010000001100000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: gray; background-position: initial initial; background-repeat: initial initial;">000</span> 80010300 2147549952
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">111</span>10000000000000010000001100000 f0002060 4026540128
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
When the leftmost bit is 0, then all of the news bits are 0:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span></span> value = 0x40010300;
print(value);
print(value >> 3);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><u style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">0</u>1000000000000010000001100000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: gray; background-position: initial initial; background-repeat: initial initial;">000</span> 40010300 1073808128
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">000</span>01000000000000010000001100000 08002060 134226016
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Unsigned right-shift operator:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">>>></code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator works similarly to the regular right-shift operator. The
difference is that the new leftmost bits are always 0 regardless of the type of
the expression and the value of the leftmost bit:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> value = 0x80010300;
print(value);
print(value <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">>>></span> 3);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">10000000000000010000001100000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: gray; background-position: initial initial; background-repeat: initial initial;">000</span> 80010300 2147549952
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">000</span>10000000000000010000001100000 10002060 268443744
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Left-shift operator:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;"><<</code></h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This operator works as the reverse of the right-shift operator. The bits are
shifted to the left:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 123456789;
print(value);
print(value <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;"><<</span> 4);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The bits on the left-hand side are lost and the new bits on the right-hand side
are 0:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: gray; background-position: initial initial; background-repeat: initial initial;">0000</span>0111010110111100110100010101 075bcd15 123456789
0111010110111100110100010101<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">0000</span> 75bcd150 1975308624
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Operators with assignment</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
All of the operators above have assignment counterparts:<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">~=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">|=</code>,<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">^=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">>>=</code>,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">>>>=</code>,
and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;"><<=</code>.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Similar to the operators that we have seen in<span class="Apple-converted-space"> </span><a href="http://ddili.org/ders/d.en/operator_overloading.html" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: purple; text-decoration: none; background-position: initial initial; background-repeat: initial initial;">the
Operator Overloading chapter</a>, these operators assign the result back to the
left-hand operand.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Let's see this on the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&=</code><span class="Apple-converted-space"> </span>operator:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> value = value & 123;
value &= 123; <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// the same as above
</span></pre>
<h5 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.25em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Semantics</h5>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Merely understanding how these operators work at bit-level may not be sufficient
to see how they are useful in programs. The following sections describe common
ways that these operators are used in.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
|</code><span class="Apple-converted-space"> </span>is a union set</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">|</code><span class="Apple-converted-space"> </span>operator
produces the union of the 1 bits in the two expressions.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As an extreme example, let's consider two values that both have alternating bits
set to 1. The union of these values would produce a result where all of the bits
are 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> lhs = 0xaaaaaaaa;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> rhs = 0x55555555;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(rhs);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"| --------------------------------"</span>);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs | rhs);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> 10101010101010101010101010101010 aaaaaaaa 2863311530
01010101010101010101010101010101 55555555 1431655765
| --------------------------------
11111111111111111111111111111111 ffffffff 4294967295
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
&</code><span class="Apple-converted-space"> </span>is an intersection set</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&</code><span class="Apple-converted-space"> </span>operator
produces the intersection of the 1 bits in the two expressions.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As an extreme example, let's consider the last two values again. Since none of
the 1 bits of the previous two expressions match the ones in the other
expression, all of the bits of the result are 0:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> lhs = 0xaaaaaaaa;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> rhs = 0x55555555;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(rhs);
writeln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"& --------------------------------"</span>);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">" "</span>); print(lhs & rhs);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> 10101010101010101010101010101010 aaaaaaaa 2863311530
01010101010101010101010101010101 55555555 1431655765
& --------------------------------
00000000000000000000000000000000 00000000 0
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
|=</code><span class="Apple-converted-space"> </span>sets selected bits to 1</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
To understand how this works, it helps to see one of the expressions as the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">actual</i><span class="Apple-converted-space"> </span>expression
and the other expression as a<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">selector</i><span class="Apple-converted-space"> </span>for
the bits to set to 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> expression = 0x00ff00ff;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> bitsToSet = 0x10001000;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"before : "</span>); print(expression);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"to set to 1: "</span>); print(bitsToSet);
expression <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">|=</span> bitsToSet;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"after : "</span>); print(expression);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The before and after values of the bits that are affected are indicated in blue:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">before : 000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">0</span>000011111111000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">0</span>000011111111 00ff00ff 16711935
to set to 1: 00010000000000000001000000000000 10001000 268439552
after : 000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">1</span>000011111111000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">1</span>000011111111 10ff10ff 285151487
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
In a sense,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">bitsToSet</code><span class="Apple-converted-space"> </span>determines
which bits to set to 1. The other bits are not affected.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
&=</code><span class="Apple-converted-space"> </span>clears selected bits</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
One of the expressions can be seen as the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">actual</i><span class="Apple-converted-space"> </span>expression
and the other expression can be seen as a<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">selector</i><span class="Apple-converted-space"> </span>for
the bits to clear (to set to 0):</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> expression = 0x00ff00ff;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> bitsToClear = 0xffefffef;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"before : "</span>); print(expression);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"bits to clear: "</span>); print(bitsToClear);
expression <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">&=</span> bitsToClear;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"after : "</span>); print(expression);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The before and after values of the bits that are affected are indicated in blue:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">before : 00000000111<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">1</span>111100000000111<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">1</span>1111 00ff00ff 16711935
bits to clear: 11111111111011111111111111101111 ffefffef 4293918703
after : 00000000111<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">0</span>111100000000111<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">0</span>1111 00ef00ef 15663343
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
In a sense,<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">bitsToClear</code><span class="Apple-converted-space"> </span>determines
which bits to set to 0. The other bits are not affected.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">
&</code><span class="Apple-converted-space"> </span>determines whether a bit is
1 or not</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
If one of the expressions has only one bit set to 1, then it can be used to
query whether the corresponding bit of the other expression is 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> expression = 123456789;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> bitToQuery = 0x00010000;
print(expression);
print(bitToQuery);
writeln(expression <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">&</span> bitToQuery ? <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"yes, 1"</span> : <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"not 1"</span>);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The bit that is being<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">queried</i><span class="Apple-converted-space"> </span>is
indicated by blue:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">000001110101101<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">1</span>1100110100010101 075bcd15 123456789
00000000000000010000000000000000 00010000 65536
yes, 1
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Let's query another bit of the same expression by this time having another bit
of<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">bitToQuery</code><span class="Apple-converted-space"> </span>set
to 1:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> bitToQuery = 0x00001000;
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">0000011101011011110<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">0</span>110100010101 075bcd15 123456789
00000000000000000001000000000000 00001000 4096
not 1
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
When the query expression has more than one bit set to 1, then the query would
determine whether<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">all</i><span class="Apple-converted-space"> </span>of
the corresponding bits in the other expression are 1.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Right-shifting by one is the equivalent of dividing by two</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Shifting all of the bits of a value by one position to the right produces half
of the original value. The reason for this can be seen in the digit-value table
above: In that table, every bit has half the value of the bit that is on its
left.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Shifting a value to the right multiple bits at a time means dividing by 2 for
that many times. For example, right-shifting by 3 bits would divide a value by
8:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 8000;
writeln(value >> 3);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">1000
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
According to how the<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">twos
complement</i><span class="Apple-converted-space"> </span>system works,
right-shifting has the same effect on signed values:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span></span> value = -8000;
writeln(value >> 3);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">-1000
</pre>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Left-shifting by one is the equivalent of multiplying by two</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Because each bit is two times the value of the bit on its right, shifting a
value one bit to the left means multiplying that value by two:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 10;
writeln(value << 5);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Multiplying by 2 a total of 5 times is the same as multiplying by 32:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">320
</pre>
<h5 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.25em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Common uses</h5>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Flags</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Flags are single-bit independent data that are kept together in the same
variable. As they are only one bit wide each, they are suitable for representing
binary concepts like enabled/disabled, valid/invalid, etc.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Such one-bit concepts are sometimes encountered in D modules that are based on C
libraries.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Flags are usually defined as non-overlapping values of an<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">enum</code><span class="Apple-converted-space"> </span>type.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
As an example, let's consider a car racing game where the realism of the game is
configurable:</p>
<ul style="margin: 0.5em 1em 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
The fuel consumption is realistic or not.</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Collisions can damage the cars or not.</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Tires can deteriorate by use or not.</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Skid marks are left on the road surface or not.</li>
</ul>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
These configuration options can be specified at run time by the following<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">enum</code><span class="Apple-converted-space"> </span>values:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">enum</span> Realism
{
fuelUse = 1 << 0,
bodyDamage = 1 << 1,
tireUse = 1 << 2,
skidMarks = 1 << 3
}
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Note that all of those values consist of single bits that do not conflict with
each other. Each value is determined by left-shifting 1 by a different number of
bits. The corresponding bit representations are the following:</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">fuelUse : 0001
bodyDamage: 0010
tireUse : 0100
skidMarks : 1000
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Since their 1 bits do not match others', these values can be combined by the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">|</code><span class="Apple-converted-space"> </span>operator
to be kept in the same variable. For example, the two configuration options that
are related to tires can be combined as in the following code:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> Realism flags = Realism.tireUse | Realism.skidMarks;
writefln(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"%b"</span>, flags);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The bits of these two flags would be side-by-side in the variable<code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">flags</code>:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">1100
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Later, these flags can be queried by the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&</code><span class="Apple-converted-space"> </span>operator:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">if</span> (flags & Realism.fuelUse) {
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ... code related to fuel consumption ...
</span> }
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">if</span> (flags & Realism.tireUse) {
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ... code related to tire consumption ...
</span> }
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&</code><span class="Apple-converted-space"> </span>operator
produces 1 only if the specified flag is set in<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">flags</code>.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Also note that the result is usable in the<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">if</code><span class="Apple-converted-space"> </span>condition
due to automatic conversion of the non-zero value to<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">true</code>.
The conditional expression is<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">false</code><span class="Apple-converted-space"> </span>when
the result of<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">&</code><span class="Apple-converted-space"> </span>is
0 and<span class="Apple-converted-space"> </span><code class="d_inline" style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 1.2em; vertical-align: baseline; background-color: transparent; font-weight: bold; color: rgb(0, 34, 34); background-position: initial initial; background-repeat: initial initial;">true</code><span class="Apple-converted-space"> </span>otherwise.
As a result, the corresponding code block is executed only if the flag is
enabled.</p>
<h6 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.1em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Masking</h6>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
In some libraries and some protocols an integer value may carry more than one
piece of information. For example, the upper 3 bits of a 32-bit value may have a
certain meaning, while the lower 29 bits may have another meaning. These
separate parts of data can be extracted from the variable by masking.</p>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The four octets of an IPv4 address are an example of this concept. The octets
are the individual values that make up the common dotted representation of an
IPv4 address. They are all kept in a single 32-bit value. For example, the IPv4
address 192.168.1.2 is the 32-bit value 0xc0a80102:</p>
<pre class="mono" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">c0 == 12 * 16 + 0 = 192
a8 == 10 * 16 + 8 = 168
01 == 0 * 16 + 1 = 1
02 == 0 * 16 + 2 = 2
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
A mask consists of a number of 1 bits that would<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">cover</i><span class="Apple-converted-space"> </span>the
specific part of a variable.<span class="Apple-converted-space"> </span><i style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">"And"ing</i><span class="Apple-converted-space"> </span>the
value by the mask extracts the part of the variable that is covered by that
mask. For example, the mask value of 0x000000ff would cover the lower 8 bits of
a value:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 123456789;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> mask = 0x000000ff;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"value : "</span>); print(value);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"mask : "</span>); print(mask);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"result: "</span>); print(value & mask);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
The bits that are covered by the mask are indicated in blue. All of the other
bits are cleared:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">value : 000001110101101111001101<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">00010101</span> 075bcd15 123456789
mask : 00000000000000000000000011111111 000000ff 255
result: 000000000000000000000000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">00010101</span> 00000015 21
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Let's apply the same method to the 0xc0a80102 IPv4 address with a mask that
would cover the uppermost 8 bits:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 0xc0a80102;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> mask = 0xff000000;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"value : "</span>); print(value);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"mask : "</span>); print(mask);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"result: "</span>); print(value & mask);
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
This mask covers the uppermost 8 bits of the value:</p>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">value : <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">11000000</span>101010000000000100000010 c0a80102 3232235778
mask : 11111111000000000000000000000000 ff000000 4278190080
result: <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">11000000</span>000000000000000000000000 c0000000 3221225472
</pre>
<p style="margin: 0.75em 1em 0.75em 16px; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
However, note that the printed result is not the expected 192 but 3221225472.
That is because the masked value must also be shifted all the way to the
right-hand side. Shifting the value 24 bit positions to the right would produce
the value that those 8 bits represent:</p>
<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); color: rgb(0, 0, 0); font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;"> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> value = 0xc0a80102;
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> mask = 0xff000000;
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"value : "</span>); print(value);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"mask : "</span>); print(mask);
write(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"result: "</span>); print((value & mask) <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">>> 24</span>);
</pre>
<pre class="shell" style="margin: 0.5em 1em 1em; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(224, 224, 224); font-weight: bold; color: rgb(0, 0, 0); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">value : <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">11000000</span>101010000000000100000010 c0a80102 3232235778
mask : 11111111000000000000000000000000 ff000000 4278190080
result: 000000000000000000000000<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">11000000</span> 000000c0 <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: rgb(255, 255, 136); background-position: initial initial; background-repeat: initial initial;">192</span>
</pre>
<h5 style="margin: 1.25em 0.5em 0.5em 8px; padding: 0px; border: 0px; outline: 0px; font-size: 1.25em; vertical-align: baseline; background-color: transparent; font-family: sans-serif; font-weight: bold; color: rgb(0, 0, 51); font-style: normal; font-variant: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
Exercises</h5>
<ol style="margin: 1em 1em 0.75em 1.5em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; color: rgb(0, 0, 0); font-family: serif; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 19px; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-position: initial initial; background-repeat: initial initial;">
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Write a function that returns an IPv4 address in its dotted form:<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); background-position: initial initial; background-repeat: initial initial;">string dotted(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> address)
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ...
</span>}
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">unittest</span>
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">assert</span>(dotted(0xc0a80102) == <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: red; background-position: initial initial; background-repeat: initial initial;">"192.168.1.2"</span>);
}
</pre>
</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Write a function that converts four octet values to the corresponding 32-bit
IPv4 address:<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> ipAddress(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">ubyte</span> octet3, <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// most significant octet
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">ubyte</span> octet2,
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">ubyte</span> octet1,
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">ubyte</span> octet0) <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// least significant octet
</span>{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ...
</span>}
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">unittest</span>
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">assert</span>(ipAddress(192, 168, 1, 2) == 0xc0a80102);
}
</pre>
</li>
<li style="margin: 0.5em 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-size: 16px; vertical-align: baseline; background-color: transparent; background-position: initial initial; background-repeat: initial initial;">
Write a function that can be used for making a mask. It should start with
the specified bit and have the specified width:<pre class="d_code" style="margin: 0.5em 1em 0.75em 16px; padding: 0.5em; border: 1px dotted rgb(153, 204, 153); outline: 0px; font-size: 1em; vertical-align: baseline; background-color: rgb(255, 255, 255); background-position: initial initial; background-repeat: initial initial;"><span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">uint</span> mask(<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> lowestBit, <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">int</span> width)
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ...
</span>}
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">unittest</span>
{
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: blue; background-position: initial initial; background-repeat: initial initial;">assert</span>(mask(2, 5) ==
0b_0000_0000_0000_0000_0000_0000_0111_1100);
<span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// ↑
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// lowest bit is 2,
</span> <span style="margin: 0px; padding: 0px; border: 0px; outline: 0px; font-size: 13px; vertical-align: baseline; background-color: transparent; color: green; background-position: initial initial; background-repeat: initial initial;">// and the mask is 5-bit wide
</span>}
</pre>
</li>
</ol>
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