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GATE 2014 CS (CS3) – Question 17

Digital Logic · Boolean Algebra and Minimization · 1 mark · Multiple choice

$F(P,Q,R,S)=\sum m(0,2,5,7,8,10,13,15)$, with minterms 2,7,8,13 treated as don’t-cares. Find the minimal sum-of-products form.

  1. $Q\overline S+\overline QS$
  2. $\overline Q\overline S+QS$
  3. $\overline Q\overline R\overline S+\overline QR\overline S+Q\overline RS+QRS$
  4. $\overline P\overline Q\overline S+\overline PQS+PQS+P\overline Q\overline S$

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Correct answer: (B) $\overline Q\overline S+QS$

Explanation

Use the don’t-care entries to form the four-cell groups with Q=0,S=0and with Q=1,S=1. P and R vary freely in each group and disappear. The result is **Q̄S̄+QS,B**, an XNOR of QandS. Don’t-cares may be assigned to help grouping.