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| 22 | <title>Bitwise Operations (GNU C Language Manual)</title>
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| 31 | <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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| 32 | <link href="Arithmetic.html" rel="up" title="Arithmetic">
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| 57 | <body lang="en">
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| 58 | <span id="Bitwise-Operations"></span><div class="header">
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| 59 | <p>
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| 60 | Previous: <a href="Shift-Operations.html" accesskey="p" rel="prev">Shift Operations</a>, Up: <a href="Arithmetic.html" accesskey="u" rel="up">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 61 | </div>
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| 62 | <hr>
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| 63 | <span id="Bitwise-Operations-1"></span><h3 class="section">6.8 Bitwise Operations</h3>
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| 64 | <span id="index-bitwise-operators"></span>
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| 65 | <span id="index-operators_002c-bitwise"></span>
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| 66 | <span id="index-negation_002c-bitwise"></span>
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| 67 | <span id="index-conjunction_002c-bitwise"></span>
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| 68 | <span id="index-disjunction_002c-bitwise"></span>
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| 69 |
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| 70 | <p>Bitwise operators operate on integers, treating each bit independently.
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| 71 | They are not allowed for floating-point types.
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| 72 | </p>
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| 73 | <p>The examples in this section use binary constants, starting with
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| 74 | ‘<samp>0b</samp>’ (see <a href="Integer-Constants.html">Integer Constants</a>). They stand for 32-bit integers
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| 75 | of type <code>int</code>.
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| 76 | </p>
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| 77 | <dl compact="compact">
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| 78 | <dt><code>~<code>a</code></code></dt>
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| 79 | <dd><p>Unary operator for bitwise negation; this changes each bit of
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| 80 | <code>a</code> from 1 to 0 or from 0 to 1.
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| 81 | </p>
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| 82 | <div class="example">
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| 83 | <pre class="example">~0b10101000 ⇒ 0b11111111111111111111111101010111
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| 84 | ~0 ⇒ 0b11111111111111111111111111111111
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| 85 | ~0b11111111111111111111111111111111 ⇒ 0
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| 86 | ~ (-1) ⇒ 0
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| 87 | </pre></div>
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| 88 |
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| 89 | <p>It is useful to remember that <code>~<var>x</var> + 1</code> equals
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| 90 | <code>-<var>x</var></code>, for integers, and <code>~<var>x</var></code> equals
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| 91 | <code>-<var>x</var> - 1</code>. The last example above shows this with -1
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| 92 | as <var>x</var>.
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| 93 | </p>
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| 94 | </dd>
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| 95 | <dt><code><code>a</code> & <code>b</code></code></dt>
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| 96 | <dd><p>Binary operator for bitwise “and” or “conjunction.” Each bit in
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| 97 | the result is 1 if that bit is 1 in both <code>a</code> and <code>b</code>.
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| 98 | </p>
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| 99 | <div class="example">
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| 100 | <pre class="example">0b10101010 & 0b11001100 ⇒ 0b10001000
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| 101 | </pre></div>
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| 102 |
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| 103 | </dd>
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| 104 | <dt><code><code>a</code> | <code>b</code></code></dt>
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| 105 | <dd><p>Binary operator for bitwise “or” (“inclusive or” or
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| 106 | “disjunction”). Each bit in the result is 1 if that bit is 1 in
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| 107 | either <code>a</code> or <code>b</code>.
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| 108 | </p>
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| 109 | <div class="example">
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| 110 | <pre class="example">0b10101010 | 0b11001100 ⇒ 0b11101110
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| 111 | </pre></div>
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| 112 |
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| 113 | </dd>
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| 114 | <dt><code><code>a</code> ^ <code>b</code></code></dt>
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| 115 | <dd><p>Binary operator for bitwise “xor” (“exclusive or”). Each bit in
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| 116 | the result is 1 if that bit is 1 in exactly one of <code>a</code> and <code>b</code>.
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| 117 | </p>
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| 118 | <div class="example">
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| 119 | <pre class="example">0b10101010 ^ 0b11001100 ⇒ 0b01100110
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| 120 | </pre></div>
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| 121 | </dd>
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| 122 | </dl>
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| 123 |
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| 124 | <p>To understand the effect of these operators on signed integers, keep
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| 125 | in mind that all modern computers use two’s-complement representation
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| 126 | (see <a href="Integer-Representations.html">Integer Representations</a>) for negative integers. This means
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| 127 | that the highest bit of the number indicates the sign; it is 1 for a
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| 128 | negative number and 0 for a positive number. In a negative number,
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| 129 | the value in the other bits <em>increases</em> as the number gets closer
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| 130 | to zero, so that <code>0b111<span class="roman">…</span>111</code> is -1 and
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| 131 | <code>0b100<span class="roman">…</span>000</code> is the most negative possible integer.
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| 132 | </p>
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| 133 | <p><strong>Warning:</strong> C defines a precedence ordering for the bitwise
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| 134 | binary operators, but you should never rely on it. You should
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| 135 | never rely on how bitwise binary operators relate in precedence to the
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| 136 | arithmetic and shift binary operators. Other programmers don’t
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| 137 | remember this precedence ordering, so always use parentheses to
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| 138 | explicitly specify the nesting.
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| 139 | </p>
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| 140 | <p>For example, suppose <code>offset</code> is an integer that specifies
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| 141 | the offset within shared memory of a table, except that its bottom few
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| 142 | bits (<code>LOWBITS</code> says how many) are special flags. Here’s
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| 143 | how to get just that offset and add it to the base address.
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| 144 | </p>
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| 145 | <div class="example">
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| 146 | <pre class="example">shared_mem_base + (offset & (-1 << LOWBITS))
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| 147 | </pre></div>
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| 148 |
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| 149 | <p>Thanks to the outer set of parentheses, we don’t need to know whether
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| 150 | ‘<samp>&</samp>’ has higher precedence than ‘<samp>+</samp>’. Thanks to the inner
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| 151 | set, we don’t need to know whether ‘<samp>&</samp>’ has higher precedence than
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| 152 | ‘<samp><<</samp>’. But we can rely on all unary operators to have higher
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| 153 | precedence than any binary operator, so we don’t need parentheses
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| 154 | around the left operand of ‘<samp><<</samp>’.
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| 155 | </p>
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| 156 | <hr>
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| 157 | <div class="header">
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| 158 | <p>
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| 159 | Previous: <a href="Shift-Operations.html" accesskey="p" rel="prev">Shift Operations</a>, Up: <a href="Arithmetic.html" accesskey="u" rel="up">Arithmetic</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 160 | </div>
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