Power of Two - The Bit Pattern

A power of two has exactly one 1 bit in its binary representation. You already know a trick to count 1 bits: $n \& (n - 1)$ flips the rightmost 1 to 0.

If $n$ is a power of two, it has one 1 bit. Flipping that bit gives 0. So $n \& (n - 1) = 0$ if and only if $n$ is a power of two (and $n > 0$, because 0 is not a power of two).

Example: $16 = 10000$. $16 - 1 = 15 = 01111$. $16 \& 15 = 00000 = 0$. For $6 = 110$: $6 - 1 = 5 = 101$. $6 \& 5 = 100 \neq 0$. This test is $O(1)$ and uses one bitwise operation.