Q. Explain about 4-bit adder-subtractor circuit?

Subtraction operation on binary numbers can be obtained by succession of addition operations only it implies that to achieve subtraction A-B we can find 2's complement of B. This can be computed by 1's complemented and then adding 1 to it. So a common circuit can carry out addition and subtraction operation. A 4-bit adder subtraction circuit is displayed in figure below that is formed by employing XOR gate with each full adder. XOR gate with output 0 is for inspecting overflow.

Figure: 4-bit adder-subtractor circuit

Control input 'x' controls operations it implies that if x =0 then circuit acts as an adder and if x =1 then circuit acts as a subtractor. The operation is summarized as below:

a. When x = 0, c = 0, output of all XOR gates would be same as corresponding input B_i where i = 0 to 3. So A_i and B_i are added by full adders providing Sum S_i and carry C_i .

b. When x = 1 output of all XOR gates will be complement of input B_i where i =0 to 3 to that carry C₀=1 is added. So circuit finds A plus 2's complement of B which is equal to A-B.