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   9 <title>section 2.9: Bitwise Operators</title>
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  15 <H2>section 2.9: Bitwise Operators</H2>
  16
  17 page 48
  18 <p>The bitwise operators are definitely a bit
  19 (pardon the pun)
  20 more esoteric than the parts of C we've covered so far
  21 (and, indeed, than probably most of C).
  22 We won't concentrate on them,
  23 but they do come up all the time,
  24 so you should
  25 eventually learn
  26 enough about them to recognize what they do,
  27 even if you don't use them in any of your own programs for a while.
  28 You may skip this section for now, though.
  29 </p><p>To see what the bitwise operators are doing,
  30 it may help to convert to binary for a moment and look at
  31 what's happening to the individual bits.
  32 In the example on page 48, suppose that <TT>n</TT> is 052525,
  33 which is 21845 decimal, or 101010101010101 binary.
  34 Then <TT>n &amp; 0177</TT>,
  35 in base 2 and base 8 (binary and octal)
  36 looks like
  37 <pre>     101010101010101     052525
  38         &amp; 000000001111111   &amp; 000177
  39           ---------------     ------
  40                   1010101        125
  41 </pre></p><p>In the second example,
  42 if <TT>SET_ON</TT> is 012
  43 and <TT>x</TT> is 0,
  44 then <TT>x | SET_ON</TT> looks like
  45 <pre>           000000000     000000
  46               | 000001010   | 000012
  47                 ---------     ------
  48                      1010         12
  49 </pre>and if <TT>x</TT> starts out as 402,
  50 it looks like
  51 <pre>           100000010     000402
  52               | 000001010   | 000012
  53                 ---------     ------
  54                 100001010        412
  55 </pre>Note that with <TT>&amp;</TT>,
  56 anywhere we have a 0 we turn bits off,
  57 and anywhere we have a 1
  58 we copy bits through from the other side.
  59 With <TT>|</TT>,
  60 anywhere we have a 1 we turn bits on,
  61 and anywhere we have a 0 we leave bits alone.
  62 </p><p>You'll frequently see the word <dfn>mask</dfn> used,
  63 both as a noun and a verb.
  64 You can imagine that we've cut a mask or stencil out of cardboard,
  65 and are using spray paint to spray through the mask
  66 onto some other piece of paper.
  67 For <TT>|</TT>, the holes in the mask are like 1's,
  68 and the spray paint is like 1's,
  69 and we paint more 1's onto the underlying paper.
  70 (If there was already paint under a hole,
  71 nothing really changes if we get more paint on it;
  72 it's still a ``1''.)
  73 </p><p>The <TT>&amp;</TT> operator is a bit harder to fit into this analogy:
  74 you can either imagine that the holes in the mask are 1's
  75 and you're spraying some preservative
  76 which will fix some of the underlying bits
  77 after which the others will get washed off,
  78 or you can imagine that the holes in the mask are 0's,
  79 and you're spraying some erasing paint or some background color
  80 which obliterates anything
  81 (i.e. any 1's, any foreground color)
  82 it reaches.
  83 </p><p>For a bit more information on ``bitwise'' operations,
  84 see the handout,
  85 ``A Brief Refresher on Some Math Often Used in Computing.''
  86 </p><p>page 49
  87 </p><p>Work through the example at the top of the page,
  88 and convince yourself that <TT>1 &amp; 2</TT> is 0
  89 and that <TT>1 &amp;&amp; 2</TT> is 1.
  90 </p><p>The precedence of the bitwise operators is not what you might expect,
  91 and explicit parentheses are often needed,
  92 as noted in this deep sentence from page 52:
  93 <blockquote>Note that the precedence of the bitwise operators
  94 <TT>&amp;</TT>, <TT>^</TT>, and <TT>|</TT>
  95 falls below <TT>==</TT> and <TT>!=</TT>.
  96 This implies that bit-testing expressions like
  97 <pre>   if ((x &amp; MASK) == 0) ...
  98 </pre>must be fully parenthesized to give proper results.
  99 </blockquote></p><hr>
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