# Binary Adder-Subtractor

The Subtraction micro-operation can be done easily by taking the 2â€™s compliment of addend bits and adding it to the augend bits.

#### Note: The 2â€™s compliment can be obtained by taking the 1â€™s compliment and adding one to the least significant pair of bits. The 1â€™s compliment can be implemented with inverters, and one can be added to the sum through the input carry.

The Arithmetic micro-operations like addition and subtraction can be combined into one common circuit by including an exclusive-OR gate with each full adder.

The block diagram for a 4-bit adder-subtractor circuit can be represented as:

- When the mode input (M) is at a low logic, i.e. â€˜0â€™, the circuit act as an adder and when the mode input is at a high logic, i.e. â€˜1â€™, the circuit act as a subtractor.
- The exclusive-OR gate connected in series receives input M and one of the inputs B.
- When M is at a low logic, we have BâŠ• 0 = B.

The full-adders receive the value of B, the input carry is 0, and the circuit performs A plus B. - When M is at a high logic, we have BâŠ• 1 = Bâ€™ and C0 = 1.

The B inputs are complemented, and a 1 is added through the input carry. The circuit performs the operation A plus the 2â€™s complement of B.

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