Question

A full subtractor can be implemented with no. of half subtractors and no. of OR gates.

• A. 3 and 1
• B. 2 and 1
• C. 3 and 2
• D. 1 and 1

Hint:

This rule is consistent for both adders and subtractors: Full Adder = 2 Half Adders + 1 OR gate. Full Subtractor = 2 Half Subtractors + 1 OR gate.

Answer 1

The Correct Option is B

A full subtractor is a combinational circuit that performs subtraction on three bits: the minuend, subtrahend, and a borrow from a previous stage. 1. Composition of a Full Subtractor: Similar to how a full adder is built from two half adders and an OR gate, a full subtractor follows a parallel structural logic.

• First Half Subtractor: Subtracts the first two bits ($A$ and $B$), producing a partial difference ($D_1$) and a partial borrow ($B_1$).

• Second Half Subtractor: Subtracts the third bit (Borrow-in, $B_{in}$) from the partial difference ($D_1$). The output of this second stage is the final

Difference ($D$). It also produces a second partial borrow ($B_2$).

2. Final Borrow Logic: The final

Borrow-out ($B_{out}$) must be high if either the first stage or the second stage produced a borrow. Therefore, the two partial borrows ($B_1$ and $B_2$) are combined using an OR gate.

3. Conclusion: To realize a full subtractor, you need

2 half subtractors and

1 OR gate.