Count Bits - Checking Each Bit

One way to count 1 bits: check each of the 32 bits individually. Use a mask (a number with one bit set) and the AND operation to test if that bit is 1.

The AND operation ($\&$) returns 1 only when both bits are 1. So $n \& 1$ checks the rightmost bit. If the result is nonzero, that bit is 1. Then shift $n$ right by 1 to check the next bit.

Repeat 32 times (for a 32-bit integer). Each iteration checks one bit and shifts. This works but is not the fastest method. There is a clever trick that processes only the 1 bits.