Official PYQ · 1999Q1.8Minimization (K-Maps etc.)MCQ1 mark

GATE CS 1999 Q1.8 — Minimization (K-Maps etc.)

Which of the following functions implements the Karnaugh map shown below?

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Answer: B

To find the Boolean function implemented by the Karnaugh map, we identify the groups of 1s (prime implicants):

First Group (Vertical Quad): A column of four 1s under the column $CD = 11$ . This simplifies to:
$\text{Term}_1 = CD$
Second Group ( $2 \times 2$ Quad): A group of four 1s located at the intersection of rows where $A = 1$ (rows $11$ and $10$ ) and columns where $D = 1$ (columns $01$ and $11$ ). This simplifies to:
$\text{Term}_2 = AD$

Combining these two terms, the simplified Boolean expression is:

\begin{aligned}F &= CD + AD \\&= D(C + A)\end{aligned}

This matches Option B.

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Published 10 Oct 2026

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