GATE 2014 EC (EC3) – Question 51

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple choice

W and Y are the most significant control-input bits of the respective multiplexers shown. Find output F.

Diagram for GATE 2014 EC (EC3) question 51

$W\overline X+\overline WX+\overline Y\overline Z$
$W\overline X+\overline WX+\overline YZ$
$W\overline X\overline Y+\overline WX\overline Y$
$(\overline W+\overline X)\overline Y\overline Z$

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Show answer and explanation

Correct answer: (C) $W\overline X\overline Y+\overline WX\overline Y$

Explanation

The first MUX inputs are0,1,1,0for selectors WX=00,01,10,11, so Q=W̄X+WX̄. The second MUX connects Q to both inputs selected when Y=0and ground to both selected when Y=1; Z has no effect. Thus **F=(W̄X+WX̄)Ȳ,C**.