GATE | Gate IT 2005 | Question 7

Which of the following expressions is equivalent to (A⊕B)⊕C
(A) (A+B+C)(A¯+B¯+C¯)
(B) (A+B+C)(A¯+B¯+C)
(C) ABC+A¯(B⊕C)+B¯(A⊕C)
(D) None


Answer: (C)

Explanation:

(A ⊕ B) ⊕ C

By Solving, We get
= (A ⊕ B)′ C + (A ⊕ B) C′

The above expression can be written as:
= (A ⊙ B) C + (A ⊕ B) C′

Now,

= (AB + A′B′) C + (A ⊕ B) C′

= ABC + A′B′C + AB′C′ + A′BC′         [As: X + X = X]                     
                     [So, A′B′C + A′B′C = A′B′C]
= ABC + (A′B′C + A′B′C) + AB′C′ + A′BC′

This can be written as:

= ABC + A′ (B ⊕ C) + B′ (A ⊕ C)

This explanation has been provided by Saksham Seth.

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