Two's Complement

What is two’s complement?

Two’s complement is the most widely used representation of signed numbers. It provides ease of representation and computation. Unlike one’s complement, two’s complement has a unique representation for 0. Two’s complement representation also has a sign bit on the extreme left.

Because there’s a unique representation of $0$, the range of two’s complement is larger than one’s complement. The $0$ comes from the positive side representation, so the range of an $n$-bit two’s complement number is: -$2^{n-1}$ to $2^{n-1}-1$. Note that $n$ is usually a power of $2$.