GATE EC 2018 Set 1 — Question 41
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Digital Circuits → Combinational Logic → MUX, DEMUX, Decoders & Encoders
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Question
A four-variable Boolean function is realized using multiplexers as shown in the figure.
The minimized expression for
F(U, V, W, X) isCorrect answer
(C) (UV + UV)W
Solution
Step 1: Analyze the first MUX.
The select lines are and . The inputs are (ground), (), (), and (ground).
The output of the first MUX, let's call it , is:
.Step 2: Analyze the second MUX.
The select lines are and . The inputs are , , (ground), and (ground).
The output
.Step 3: Substitute back into the expression for .
.
This matches option (C).
The select lines are and . The inputs are (ground), (), (), and (ground).
The output of the first MUX, let's call it , is:
.Step 2: Analyze the second MUX.
The select lines are and . The inputs are , , (ground), and (ground).
The output
F(U, V, W, X) is:.Step 3: Substitute back into the expression for .
.
This matches option (C).
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