Toggling a Bit

To toggle bit $k$ (flip 0 to 1 or 1 to 0) in number $n$, you XOR $n$ with $2^k$. In code: $n \wedge (1 << k)$.

XOR flips bits because $0 \wedge 1 = 1$ and $1 \wedge 1 = 0$. When you XOR with a 1, that bit flips. When you XOR with a 0, the bit stays the same.

Example: Toggle bit 1 in $12 = 1100$. Compute $12 \wedge 2 = 1100 \wedge 0010 = 1110 = 14$. Bit 1 flipped from 0 to 1. Toggle again: $14 \wedge 2 = 1100 = 12$. It's back.