GATE EC 2017 Set 1 — Question 43
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Digital Circuits → Combinational Logic → Canonical SOP & POS
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Question
Which one of the following gives the simplified sum of products expression for the Boolean function , where and are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
Correct answer
(B) A C + AB + ABC
Solution
with as MSB: the 1-cells are .K-map grouping:
- ( with varying) →
- →
- has no adjacent 1 ( are 0) →
- (A) and (D) also equal , but each contains a 3-literal term ( or ) where a 2-literal prime implicant suffices, so they are not simplified.
- (C) contains , which covers (100) where , so it is not even equal to .
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