GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 21

Let ⊕ and ⊙ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following Boolean expression is equivalent to given expression?

(A ⊕ B)(C ⊙ D) + (A ⊙ B)(C ⊕ D) 

(A) A ⊙ B ⊙ C ⊙ D
(B) A ⊕ B ⊙ C ⊕ D
(C) A ⊙ B ⊕ C ⊙ D
(D) A ⊕ B ⊕ C ⊕ D


Answer: (D)

Explanation:

= (A ⊕ B)(C ⊙ D) + (A ⊙ B)(C ⊕ D)
= (A ⊕ B)(C ⊕ D)' + (A ⊕ B)'(C ⊕ D)
= (A ⊕ B) ⊕ (C ⊕ D)
= A ⊕ B ⊕ C ⊕ D 

Option (D) is correct.

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