The addition and subtraction operations can be done using an Adder-Subtractor circuit. The figure shows the logic diagram of a 4-bit Adder-Subtractor circuit.

The circuit has a mode control signal M which determines if the circuit is to operate as an adder or a subtractor.

Each XOR gate receives input M and one of the inputs of B, i.e., B

_{i}. To understand the behavior of XOR gate consider its truth table given below. If one input of XOR gate is zero then the output of XOR will be same as the second input. While if one input of XOR gate is one then the output of XOR will be complement of the second input.So when M = 0, the output of XOR gate will be B

_{i }⊕ 0 = B_{i}.If theWhen M = 1, the output of XOR gate will be B

_{i }⊕ 1 = B_{i}^{’}. If the full adders receive the value of B’, and the input carry C_{0 }is 1, the circuit performs A plus 1’s complement of B plus 1, which is equal to A minus B.
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