Given two non-negative integers a and b, count how many bit positions need to be flipped to turn a into b. A bit position needs flipping exactly where a and b disagree — and XOR is built to flag exactly that: a ^ b has a 1 in every position where the two numbers differ, and a 0 everywhere they agree. Counting the set bits in that XOR result, the same set-bit-counting trick used earlier, gives the answer directly.