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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