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.

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