title: Construction an logical expression which will count bits in a byte
body: <p>When interviewing new candidates, we usually ask them to write a piece of C code to count the number of bits with value 1 in a given byte variable (e.g. the byte 3 has two 1-bits). I know all the common answers, such as right shifting eight times, or indexing constant table of 256 precomputed results.  </p>
  
  <p>But, is there a  smarter way without using the precomputed table? What is the shortest combination of byte operations (AND, OR, XOR, +, -, binary negation, left and right shift) which computes the number of 1-bits?</p>