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GATE 2026 CS (CS2) – Question 40

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

Consider the 4-variable Boolean function
$$F(A,B,C,D)=\Sigma m(0,1,2,3,8,9,10,11).$$
Taking $A$ as MSB and $D$ as LSB, which one of the following represents the minimal sum-of-products form?

  1. $A' + B' + C' + D'$
  2. $B'$
  3. $A'B' + AB$
  4. $A'$

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Correct answer: (B) $B'$

Explanation

The minterms 0-3 and 8-11 correspond exactly to all combinations where $B=0$, regardless of the values of $A$, $C$, and $D$. Therefore, the function simplifies to $F=B'$. Hence the minimal sum-of-products form is option (B).