Which of the following statements is/are true about Half-Subtractor? (i) D =…
2022
Which of the following statements is/are true about Half-Subtractor?
(i) D = x⊕y, where D is difference, and x, y are inputs.
(ii) B = xy, where B is borrow, and x, y are inputs.
Answer: A. Only (i) — ConceptA half-subtractor subtracts one binary bit (subtrahend y) from another (minuend x), producing two outputs: the Difference (D) and the Borrow (B). By…
- A.
Only (i)
- B.
Only (ii)
- C.
Both (i) and (ii)
- D.
Neither (i) nor (ii)
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Show answer & explanation
Correct answer: A
Concept
A half-subtractor subtracts one binary bit (subtrahend y) from another (minuend x), producing two outputs: the Difference (D) and the Borrow (B). By definition the Difference is the XOR of the inputs, D = x ⊕ y, and the Borrow is asserted only when a 0 has 1 subtracted from it, giving B = x' · y (NOT-x AND y).
Application
Build the truth table for every input combination of x and y:
x | y | D = x ⊕ y | B (actual borrow) |
|---|---|---|---|
0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 0 |
Reading the columns: D is 1 exactly when x and y differ, which matches x ⊕ y. The borrow B is 1 only in the row x = 0, y = 1, which is exactly x' · y.
Evaluate the two statements
Statement (i): D = x ⊕ y. This matches the Difference column exactly, so (i) is true.
Statement (ii): B = xy (plain AND). Plain AND gives 1 only when x = 1 and y = 1, but the borrow column shows 1 at x = 0, y = 1. So B = xy is false; the correct borrow is x' · y. (B = xy is actually the carry of a half-adder, not the borrow of a half-subtractor.)
Cross-check
Difference holds; borrow as written (xy) does not. Hence exactly one statement is valid — statement (i) only.