GATE | Gate IT 2005 | Question 7
Which of the following expressions is equivalent to (A⊕B)⊕C
(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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