# Adder–subtractor

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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.

## Role in the arithmetic logic unit

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Adders are a part of the core of an arithmetic logic unit (ALU). The control unit decides which operations an ALU should perform (based on the op code being executed) and sets the ALU operation. The input to the adder–subtractor above would be one such control line from the control unit.

The adder–subtractor above could easily be extended to include more functions. For example, a 2-to-1 multiplexer could be introduced on each that would switch between zero and ; this could be used (in conjunction with ) to yield the two's complement of since .

A further step would be to change the 2-to-1 mux on to a 4-to-1 with the third input being zero, then replicating this on thus yielding the following output functions:

- (with the both and input set to zero and )
- (with the both and input set to zero and )
- (with the input set to zero)
- (with the input set to zero)
- (with the input set to zero and )
- (with the input set to zero and )
- (with set to invert; set to zero; and )
- (with set to invert; set to zero; and )
- (with set to invert; set to zero; and )
- (with set to invert; set to zero; and )

By adding more logic in front of the adder, a single adder can be converted into much more than just an adder—an ALU.