GATE CS 2026 Set 2 Q.40: Boolean Algebra and Logic Minimization

Consider the following 4-variable Boolean function

F(A, B, C, D) = \Sigma m(0, 1, 2, 3, 8, 9, 10, 11)

Consider $A$ as MSB, $D$ as LSB. Which one of the following options represents the minimal sum of products form for the above function?

Note: $+$ is OR operation, $.$ is AND operation, $'$ is NOT operation

$A' + B' + C' + D'$

$B'$

$A' . B' + A . B$

$A'$

Official answer and solution

Solution

Examine the binary representations of minterms $0..3$ and $8..11$ .

In 4-bit binary $(A, B, C, D)$ :

Minterms $0, 1, 2, 3$ correspond to $A = 0, B = 0$ and all 4 combinations of $(C, D)$ .
Minterms $8, 9, 10, 11$ correspond to $A = 1, B = 0$ and all 4 combinations of $(C, D)$ .

Together, these 8 minterms cover all combinations where $B = 0$ :

F(A, B, C, D) = A'B' + AB' = (A' + A)B' = B'

Final answer

Option (B)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 40 of 65
Section: Computer Science and Information Technology

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