The GATE Grind

GATE 2025 CS (CS2) – Question 31

Digital Logic · Combinational Circuits · 1 mark · Multiple select

Consider the following logic circuit diagram.

[Figure: inputs $X$ and $Y$ feed a NAND gate, a NOT gate on $X$, and an AND gate taking $X$ and $\bar{Y}$; the three outputs feed a 3-input OR gate producing $F$.]

Which is/are the CORRECT option(s) for the output function $F$?

Diagram for GATE 2025 CS (CS2) question 31
  1. $\overline{XY}$
  2. $\bar{X} + \bar{Y} + X\bar{Y}$
  3. $\overline{XY} + \bar{X} + X\bar{Y}$
  4. $X + \bar{Y}$

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Show answer and explanation

Correct answer: (A) $\overline{XY}$; (B) $\bar{X} + \bar{Y} + X\bar{Y}$; (C) $\overline{XY} + \bar{X} + X\bar{Y}$

Explanation

$F = \overline{XY} + \bar{X} + X\bar{Y} = \bar{X} + \bar{Y} + \bar{X} + X\bar{Y} = \bar{X} + \bar{Y}$. Options A, B and C all simplify to $\bar{X}+\bar{Y}$, while D does not.