GATE EC 2015 Set 2 — Question 46
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Digital Circuits → Combinational Logic → Canonical SOP & POS
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Question
A function of Boolean variables X, Y and Z is expressed in terms of the min-terms asF(X, Y, Z) = Σ (1, 2, 5, 6, 7)Which one of the product of sums given below is equal to the function F(X, Y, Z)?
Correct answer
(B) (X+Y+Z)⋅(X+Y+Z)⋅(X+Y+Z)
Solution
Since , the minterms absent are , soA maxterm complements each variable that is 1 in its index:
- (000):
- (011):
- (100):
- (A) , i.e. zeros at 3, 4, 7 — but is in . Wrong.
- (C) — zeros at minterms that belong to . Wrong.
- (D) — again zeros at minterms of . Wrong.
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