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GATE 2017 CS (CS2) – Question 38

Digital Logic · Boolean Algebra and Minimization · 2 marks · Multiple choice

$f(w,x,y,z)=\sum m(0,1,2,3,7,8,10)+\sum d(5,6,11,15)$, with d denoting Karnaugh-map don’t-cares. Find a minimum product of sums.

  1. $(\bar w+\bar z)(\bar x+z)$
  2. $(\bar w+z)(x+z)$
  3. $(w+z)(\bar x+z)$
  4. $(w+\bar z)(\bar x+z)$

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Show answer and explanation

Correct answer: (A) $(\bar w+\bar z)(\bar x+z)$

Explanation

The specified zero minterms are 4,9,12,13,14. Group zeros 9,13 with don’t-cares 11,15, obtaining w=1,z=1 and sum term (w̄+z̄). Group 4,12,14 with don’t-care 6, obtaining x=1,z=0 and term (x̄+z). Their product is A. Each maximal group removes two variables, giving a minimum two-factor POS.

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