ISRO EC 2025 Q.24: solution and answer

ISRO 2025 · ECQ.24 · 1 mark · MCQ

For a binary half subtractor having two input $A$ and $B$ , the correct set of logical expressions for outputs $D = (A - B)$ and $X$ (borrow) are

(A)
$D = A B + \overline{A} \overline{B}$ , $X = \overline{A} B$
(B)
$D = \overline{A} B + A \overline{B}$ , $X = \overline{A} B$
(C)
$D = \overline{A} B + A \overline{B}$ , $X = A \overline{B}$
(D)
$D = B + \overline{A} \overline{B}$ , $X = A \overline{B}$

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Answer and solution

ANSWER

The correct option is (b): $D = \overline{A} B + A \overline{B}$ and $X = \overline{A} B$ .

Official answer: BSource: ISRO's final answer key of 15 May 2026

A half subtractor subtracts one bit from another, $A - B$ , and produces a difference $D$ and a borrow $X$ .
Truth table for $(A, B)$ : $00 \to D = 0, X = 0$ ; $01 \to D = 1, X = 1$ (0 minus 1 gives 1 with a borrow); $10 \to D = 1, X = 0$ ; $11 \to D = 0, X = 0$ .
The difference is 1 only when the inputs differ, so $D = \overline{A} B + A \overline{B} = A \oplus B$ .
A borrow is needed only when $A = 0$ and $B = 1$ , so $X = \overline{A} B$ .
Option (a) has $D = A B + \overline{A} \overline{B}$ , which is $A ⊙ B$ (XNOR), so it is wrong.
Options (c) and (d) have $X = A \overline{B}$ , which is the borrow for $B - A$ , so the borrow is wrong. Option (d) also has the wrong $D$ , since $B + \overline{A} \overline{B} = B + \overline{A}$ .
Only option (b) has $D = \overline{A} B + A \overline{B}$ and $X = \overline{A} B$ .

KEY IDEA

A half subtractor has $D = A \oplus B$ and borrow $X = \overline{A} B$ , because a borrow occurs only for $0 - 1$ . Build the truth table first and read the expressions from it.

WATCH OUT FOR

Writing the borrow as $A \overline{B}$ , which is the borrow for $B - A$ and not for $A - B$ , or mixing up the XOR difference with the XNOR.

From the ISRO EC 2025 paper. Every question of this paper · The full paper (PDF, ISRO) · All 6 ISRO Combinational questions, with notes

ISRO EC 2025 Q.24: solution and answer

Answer and solution

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