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GATE 2026 EC – Question 48

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple choice

A Boolean function, $f(x,y,z)$ with $x$ as MSB and $z$ as LSB is realized by 4:1 multiplexer (MUX) with select lines, $S_1$ and $S_0$ ($S_1$ is MSB, $S_0$ is LSB) and inputs, $I_0$, $I_1$, $I_2$, $I_3$ as shown in the Figure. Which of the following options is the correct expression of $f(x,y,z)$?

Diagram for GATE 2026 EC question 48
  1. $xz+y$
  2. $x\bar y+z$
  3. $xy+\bar z$
  4. $\bar xy+\bar z$

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Correct answer: (C) $xy+\bar z$

Explanation

$f=\bar x\bar z(1)+\bar xz(0)+x\bar z(1)+xz\,y=\bar z+xyz=\bar z+xy$.