# Two's Complement

Learn the representation of signed numbers in binary using 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 $2$.

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