GATE 2021 CS (CS2) – Question 15

Digital Logic · Combinational Circuits · 1 mark · Multiple choice

Which 4-to-1 multiplexer implements f(x,y,z)=Σm(0,1,3,4,5,6), with select lines s1=y,s0=z?

Diagram for GATE 2021 CS (CS2) question 15

Inputs I0,I1,I2,I3 = 1,1,x,x′
Inputs I0,I1,I2,I3 = x,1,x′,1
Inputs I0,I1,I2,I3 = 1,1,x′,x
Inputs I0,I1,I2,I3 = x′,1,x,1

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Show answer and explanation

Correct answer: (A) Inputs I0,I1,I2,I3 = 1,1,x,x′

Explanation

For yz=00, both x cases are minterms zero,four, so I0=1. For yz=01, minterms one,five give I1=1. For yz=10, only x=1 (minterm six) is included, so I2=x. For yz=11, only x=0 (minterm three) is included, so I3=x′. Thus A.

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