Official PYQ · 1987Q1-IVCombinational CircuitsMCQ1 mark

GATE CS 1987 Q1-IV — Combinational Circuits

The output $F$ of the below multiplexer circuit can be represented by

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Answer: B

The given circuit is a standard $4$ -to- $1$ multiplexer (MUX) with select lines $S_1 = A$ and $S_0 = B$ .

The inputs connected to the multiplexer data lines are:

$I_0 = C$
$I_1 = \bar{C}$
$I_2 = \bar{C}$
$I_3 = C$

The output equation of a $4$ -to- $1$ multiplexer is given by:

F = \bar{A}\bar{B}I_0 + \bar{A}BI_1 + A\bar{B}I_2 + ABI_3

Substituting the input values into the equation:

F = \bar{A}\bar{B}C + \bar{A}B\bar{C} + A\bar{B}\bar{C} + ABC

This is the sum-of-minterms expansion for the $3$ -variable XOR (odd-parity) function:

F = A \oplus B \oplus C

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Published 10 Oct 2026

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