Question

Suppose there are given two integers, a and b, and we know that a>b. I want to calculate how many operations I should make on b to get a (by operation I mean that bitwise operations change a bit from 1 to 0 and vice versa. How can I count the number of operation for such a transform?

Answer 1

What you are looking is called the Hamming distance. Here is how I compute it in C/C++:

unsigned hamdist(unsigned x, unsigned y)
{
  unsigned dist = 0;
  unsigned val = x ^ y;

  // Count the number of set bits (Knuth's algorithm)
  while(val)
  {
    ++dist;
    val &= val - 1;
  }
  return dist;
}