GATE CSE 2014 | Set 3 | Question: 7

Question

Consider the following minterm expression for $F$:

$$F(P,Q,R,S) = \sum 0,2,5,7,8,10,13,15$$

The minterms $2$, $7$, $8$ and $13$ are 'do not care' terms. The minimal sum-of-products form for $F$ is

• A. $Q \bar S+ \bar QS$
• B. $ \bar Q \bar S+QS$
• C. $ \bar Q \bar R \bar S+ \bar QR \bar S+Q \bar R S+QRS$
• D. $ \bar P \bar Q \bar S+ \bar P QS+PQS+P \bar Q \bar S$

Comments

Similar question: https://gateoverflow.in/460802/gate-cse-2025-set-2-question-33#a_list

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Answer 1

While putting the terms to K-map the $3^{rd}$ and $4^{th}$ columns are swapped so, do $3^{rd}$ and 4th rows. So, term $2$ is going to $(0,3)$ column instead of $(0,2)$, $8$ is going to $(3,0)$ instead of $(2,0)$ etc.

 

Solving this k-map gives B) as the answer.

Reference: http://www.cs.uiuc.edu/class/sp08/cs231/lectures/04-Kmap.pdf