The GATE Grind

GATE 2014 CS (CS1) – Question 55

Digital Logic · Combinational Circuits · 2 marks · Multiple choice

For the 4-to-1 multiplexer shown, with select lines $S_1$ and $S_0$, find the minimal sum-of-products form of output F.

Diagram for GATE 2014 CS (CS1) question 55
  1. $\bar PQ+Q\bar R+P\bar QR$
  2. $\bar PQ+\bar PQ\bar R+PQ\bar R+P\bar QR$
  3. $\bar PQR+\bar PQ\bar R+Q\bar R+P\bar QR$
  4. $PQ\bar R$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $\bar PQ+Q\bar R+P\bar QR$

Explanation

The four select combinations yield0,1,R,R̄ for PQ=00,01,10,11. Thus F=P̄Q+PQ̄R+PQR̄. Absorb the last term with P̄Q to obtain **P̄Q+QR̄+PQ̄R,A**. Checking all four select cases confirms equivalence.