title: Do bitwise operators (other than shifts) make any mathematical sense in base-10?
body: <p>According to <a href="http://en.wikipedia.org/wiki/Arithmetic_shift" rel="noreferrer">wiki</a> shifts can be used to calculate powers of 2:</p>
  
  <blockquote>
    <p>A left arithmetic shift by n is
    equivalent to multiplying by 2^n
    (provided the value does not
    overflow), while a right arithmetic
    shift by n of a two's complement value
    is equivalent to dividing by 2^n and
    rounding toward negative infinity.</p>
  </blockquote>
  
  <p>I was always wondering if any other bitwise operators (<code>~</code>,<code>|</code>,<code>&amp;</code>,<code>^</code>) make any mathematical sense when applied to base-10? I understand how they work, but do results of such operations can be used to calculate anything useful in decimal world?</p>