GATE EE 2017 Set 1 — Question 36
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Analog & Digital Electronics → Digital Logic Circuits → K-Map Minimization
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Question
The output expression for the Karnaugh map shown below is
Correct answer
(D) BD + ABC
Solution
1.Read the 1s from the K-map:
With the rows labelled and the columns labelled , the 1s sit at , , , and .2.Group the 1s:
- Quad: , , , (columns 00 and 10 are adjacent by wrap-around). Across these four cells and are the only constants, so the quad gives .
- Pair: and . Here , , and only changes, so the pair gives .
Option (A) fails because also covers , which is 0 in the map. Option (B) fails because covers , which is 0. Option (C) covers cells with , which are all 0 in the map.Answer: (D)
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