GATE | GATE CS 2019 | Question 39
Consider three 4-variable functions f1, f2 and f3, which are expressed in sum-of-minterms
f1 = Σ(0, 2, 5, 8, 14)
f2 = Σ(2, 3, 6, 8, 14, 15)
f3 = Σ(2, 7, 11, 14)
For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:
(A) Σ(7, 8, 11)
(B) Σ(2, 14)
(C) Σ(0, 2, 3, 5, 6, 7, 8, 11, 14)
(D) Σ(2, 7, 8, 11, 14)
Answer: (A)
Explanation: According to the circuit diagram:
= f1 ∧ f2
= Σ(0, 2, 5, 8, 14) ∧ Σ(2, 3, 6, 8, 14, 15)
= Σ (2, 8, 14)
{ i.e., Common minterm }
Again,
= (f1 ∧ f2) ⊕ Σ(2, 7, 11, 14)
= Σ(2, 8, 14) ⊕ Σ(2, 7, 11, 14)
= Σ(7, 8, 11)
{ i.e., either in first set or in second set but not in both }
So, option (A) is correct.
Quiz of this Question
Last Updated :
18 Feb, 2019
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...