Bitwise complement ($\tilde{x}$)

The bitwise complement reverses every bit. In an unsigned width-$w$ representation, it sends $x$ to $(2^w-1)-x$ for $0\le x<2^w$: four-bit 0101 becomes 1010. Width is essential; without a width there is no finite all-ones mask. Python integers instead behave as infinite sign-extended two's-complement values, giving ~x = -x - 1. A width-$w$ complement in that setting is (~x) & ((1 << w) - 1). The operation is different from Boolean logical negation, which produces a truth value.^[ref]