Official PYQ · 1998Q2.7Minimization (K-Maps etc.)MCQ1 mark

GATE CS 1998 Q2.7 — Minimization (K-Maps etc.)

The function represented by the Karnaugh map given below is

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Answer: C

In a standard 3-variable Karnaugh map with row variable $A$ and column variables $BC$ (ordered as $00, 01, 11, 10$ ):

The columns corresponding to $BC = 00$ and $BC = 11$ contain $1$ s in both rows ( $A = 0$ and $A = 1$ ).
Combining the $1$ s in column $00$ gives the term $\overline{B}\overline{C}$ .
Combining the $1$ s in column $11$ gives the term $BC$ .

Summing these terms yields the simplified Boolean function:

F = \overline{B}\overline{C} + BC

Using Boolean algebra identities, this represents the XNOR operation:

F = B \odot C = \overline{B \oplus C}

Thus, the correct option is C.

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Published 10 Oct 2026

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