GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 29

G2, G3 are four variables functions which are represented as the sum-of-minterms
\newline G_{1}=\sum (2,4,5,13,15) \newline G_{2}=\sum (2,6,13,15) \newline G_{3}=\sum (0,2,7,13,15)

Y = (F1 + F2) ⊕ F3, which of the following correctly represents Y as sum-of-minterms.

(A) Y=\sum (0,4,5,6,7,15)
(B) Y=\sum (13,15)
(C) Y=\sum (0,2,13)
(D) Y=\sum (0,4,5,6,7)


Answer: (D)

Explanation: G1 + G2 is like union and will take all terms from G1 and G2 so,
G_{1}+G_{2}=\sum (2,4,5,6,13,15)
Then doing XOR operation will take all numbers which are present in only one of them ,
\newline \sum (2,4,5,6,13,15)\bigoplus G_{3} \newline =\sum (2,4,5,6,13,15)\bigoplus \sum(0,2,7,13,15) =\sum (0,4,5,6,7)

Option (D) is correct.

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