Reversing Bits

To reverse the bits of a 32-bit integer, you need to swap bit positions: bit 0 becomes bit 31, bit 1 becomes bit 30, and so on.

The approach: initialize a result to 0. For each of the 32 bits in the input, check if the bit is set. If it is, set the corresponding reversed position in the result.

For bit $i$ in the input, the reversed position is $31 - i$. Extract bit $i$ from input, then set bit $31 - i$ in result. After 32 iterations, you have the reversed number.