Aptitude | GATE CS 1998 | Question 13

What happens when a bit-string is XORed with itself n-times as shown:

[ B⊕ (B⊕ (B⊕ (B…….. n times) ]

(A) complements when n is even
(B) complements when n is odd
(C) divides by 2^n always
(D) remains unchanged when n is even


Answer: (D)

Explanation: Here n refers to the number of times XOR operation is triggered.

For example,

A⊕A⊕A = A   (Number of XOR operation is 2 ,i.e., Even)

A⊕A⊕A⊕A = 0   (Number of XOR operation is 3 ,i.e., Odd)

A⊕A⊕A⊕A⊕A = A   (Number of XOR operation is 4 ,i.e., Even)

A⊕A⊕A⊕A⊕A⊕A = 0  (Number of XOR operation is 5 ,i.e., Odd) 

In General, when the number of XOR operation is Even, the output remains unchanged, while when the number of XOR operation is Odd, the output will be 0.

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