GATE CSE 1987 | Question: 12-a

Question

The Boolean expression $A \oplus B \oplus A$ is equivalent to

• A. $AB + \overline {A}\;\;\overline B$
• B. $\overline{A}\;B+A\;\overline{B}$
• C. $B$
• D. $\overline{A}$

Comments

$\textbf{Key point:}$ Exor and Exnor are commutative as well as associative Boolean operators.

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Answer 1

Option (C)  $B$

$A\oplus A= 0$ and $0 \oplus A = A$

$A \oplus B \oplus A= ( A\oplus A) \oplus B = 0 \oplus B = \bf{B}$

Comments

Note :

$A⊕B⊕A=(A⊕A)⊕B=0⊕B=B$

We can do so because Ex-OR is Commutative and Associative Operation.

$A⊕B⊕A= A⊕(B⊕A) $ // By Associativity

$A⊕(B⊕A)  = A⊕(A⊕B) $ // By Commutativity

$A⊕(A⊕B) = (A⊕A)⊕B $ // By Associativity

$(A⊕A)⊕B = (0) ⊕ B = B$

https://youtu.be/XhKwhWzXBd0 

Answer 2

Ans:

Comments

Thnx varun raj

Answer 3

A xor A = 0

So, A xor B xor A = B xor 0 = B