GATE CS 2014 Set 3 — Question 65
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Digital Logic → Boolean Algebra & Logic Gates → Boolean Laws & Theorems
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Question
Let denote the Exclusive OR (XOR) operation. Let ‘1’ and ‘0’ denote the binary constants. Consider the following Boolean expression for over two variables and :The equivalent expression for is
Correct answer
(D) P ⊕ Q
Solution
Given the Boolean expression:We know that the XOR operation () is associative and commutative. Also, , , and .Let's simplify the expression step-by-step.Step 1: Simplify the left term
Step 2: Simplify the right term
Step 3: Combine the resultsUsing the definition of XOR ():This is the expression for the XNOR operation (equivalence), which is the complement of XOR:Thus, the equivalent expression is .
Step 2: Simplify the right term
Step 3: Combine the resultsUsing the definition of XOR ():This is the expression for the XNOR operation (equivalence), which is the complement of XOR:Thus, the equivalent expression is .
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