Setting a Bit

To set bit $k$ (make it 1) in number $n$, you OR $n$ with $2^k$. This guarantees bit $k$ becomes 1, while leaving all other bits unchanged.

The OR operation turns bits on. Since $1 | 1 = 1$ and $0 | 1 = 1$, ORing with a bit that's 1 forces that position to 1 regardless of what was there before.

Example: Set bit 1 in $12 = 1100$. Compute $12 | (1 << 1) = 12 | 2 = 1100 | 0010 = 1110 = 14$. Bit 1 is now on.