With the help of a truth table explain the working of a half subtractor. Draw the logic diagram using gates.

Ans:

Half Subtractor: For the subtraction of B (subtrahend) from A (minuend) in a logic circuit, where A and B are 1-bit numbers is termed to as a Half-Subtractor. The truth table of half subtractor is illustrated in below. Now there A and B are the two inputs and D_i that is difference and B_o that is borrow are the two outputs. If B is larger than A (for example, A=0 and B=1), a borrow is essential,

Truth Table no.1

By the Truth Table, the logical expressions for D_i and B_o are acquired as

D_i = A‾ B + A B‾

B_O = A‾ B

Fig.(a) Logic Diagram of Half Subtractor       Fig.(b) Block Diagram of Half Subtractor

In Table, input variable B is subtracted from A to provide output D_i difference. If B is larger than A (for example, A = 0 and B = 1), borrow is essential. In the Truth Table, inputs are A  and  B,  Outputs  are  D_i (difference)  and  B₀ (borrow). Therefore, the Boolean expressions for the half subtractor by the Truth Table can be written as

D_i = A ⊕ B ---------(1)

B_O = A‾ B    --------(2)

Through combining Boolean Expressions (1) and (2), we find the logic circuit for Half Subtractor demonstrated in fig.(a) and its block diagram is demonstrated in fig.(b).