Simple Example - Subset Membership

Let's ground those bit operations with a concrete example. Suppose you have $n = 4$ elements labeled $0, 1, 2, 3$. The mask $13$ in decimal equals $1101$ in binary.

Reading right to left: bit $0$ is $1$ (element $0$ included), bit $1$ is $0$ (element $1$ excluded), bit $2$ is $1$ (element $2$ included), bit $3$ is $1$ (element $3$ included).

So mask $13$ represents the subset $\{0, 2, 3\}$. Check if element $2$ is in the subset: $(13 >> 2) \& 1 = (1101 >> 2) \& 1 = 11 \& 1 = 1$. Yes, it's included. Check element $1$: $(13 >> 1) \& 1 = 110 \& 1 = 0$. Not included. These operations become automatic with practice.