Adder–subtractor

In digital circuits, an adder–subtractor is a circuit that is capable of adding or subtracting numbers (in particular, binary). Below is a circuit that does adding or subtracting depending on a control signal. It is also possible to construct a circuit that performs both addition and subtraction at the same time.

Having an n-bit adder for ${\displaystyle A}$ and ${\displaystyle B}$, then ${\displaystyle S=A+B}$. Then, assume the numbers are in two's complement. Then to perform ${\displaystyle B-A}$, two's complement theory says to invert each bit with a NOT gate then add one. This yields ${\displaystyle S=B+{\overline {A}}+1}$, which is easy to do with a slightly modified adder.

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