The GATE Grind

GATE 2026 EC – Question 56

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple select

Consider the four-variable Boolean function, $f(w,x,y,z)=\sum m(0,2,5,7,8,10,13,14,15)$ with ‘$w$’ as MSB and ‘$z$’ as LSB. Which of the following expressions is/are the valid form(s) of $f(w,x,y,z)$?

  1. $\bar x\bar z+xz+wxy$
  2. $xz+wxy+w\bar x\bar z+\bar wxy\bar z$
  3. $\bar x\bar z+wxy+w\bar x\bar z+\bar wxy\bar z$
  4. $\bar x\bar z+xz+wy\bar z$

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Show answer and explanation

Correct answer: (A) $\bar x\bar z+xz+wxy$; (D) $\bar x\bar z+xz+wy\bar z$

Explanation

$\bar x\bar z$ covers m0, 2, 8, 10; $xz$ covers m5, 7, 13, 15; the remaining m14 is covered by $wxy$ (m14, 15) or $wy\bar z$ (m10, 14). So A and D are valid. B and C contain $\bar wxy\bar z$ = m6, which is not in f, and C also lacks $xz$.