The GATE Grind

GATE 2014 EC (EC3) – Question 26

Digital Circuits · Combinatorial Circuits · 1 mark · Multiple choice

Which Boolean function does the multiplexer circuit realize?

Diagram for GATE 2014 EC (EC3) question 26
  1. $F=W\overline S_1\overline S_2$
  2. $F=WS_1+WS_2+S_1S_2$
  3. $F=\overline W+S_1+S_2$
  4. $F=W\oplus S_1\oplus S_2$

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Correct answer: (D) $F=W\oplus S_1\oplus S_2$

Explanation

A2:1multiplexer selecting W for S1=0and W̄ for S1=1produces W XOR S1. The next stage selects this result or its complement according to S2, performing another XOR. Therefore **F=W XOR S1 XOR S2,D**.