以下哪个表达式等价于 (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)无答案： (C)
解释：
(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)
这个解释由Saksham Seth 提供。
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