The GATE Grind

GATE 2025 CS (CS2) – Question 43

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

Given the following Karnaugh Map for a Boolean function $F(w,x,y,z)$ (rows $wx$ = 00, 01, 11, 10; columns $yz$ = 00, 01, 11, 10):

$wx \backslash yz$00011110
001001
010110
110110
101001

Which one or more of the following Boolean expression(s) represent(s) $F$?

  1. $\bar{w}\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}\bar{z} + \bar{w}\bar{x}y\bar{z} + w\bar{x}y\bar{z} + xz$
  2. $\bar{w}\bar{x}\bar{y}\bar{z} + \bar{w}\bar{x}y\bar{z} + w\bar{x}yz + xz$
  3. $\bar{w}\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}z + xz$
  4. $\bar{x}\bar{z} + xz$

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Show answer and explanation

Correct answer: (A) $\bar{w}\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}\bar{z} + \bar{w}\bar{x}y\bar{z} + w\bar{x}y\bar{z} + xz$; (D) $\bar{x}\bar{z} + xz$

Explanation

The map gives $F = \bar{x}\bar{z} + xz$ (minterms 0,2,8,10,5,7,13,15), which is option D. Option A's four terms combine to $\bar{x}\bar{z}$ and so equal F. B contains minterm 11 and C contains minterm 9, both of which are 0 in F.