在XOR中是独一无二的，真的适合两个以上的输入吗？

Question

What does Exclusive in XOR really mean for more than two inputs? Doesn't word Exclusive suggest only one input must be true and not odd number of inputs. Note that the inputs are in sequence. This may seem like duplicate question but all similar questions answer for only two inputs and hence causes me confusion.

Answer 1

Exclusive OR is defined for two operands only, like eg addition. Just like an addition, it happens to be associative . This means

(a xor b) xor c = a xor (b xor c)

for all inputs a , b and c .

For associative operations, it is customary to drop parentheses because they cannot change meaning of an expression:

(a + b) + c = a + (b + c) = a + b + c
(a xor b) xor c = a xor (b xor c) = a xor b xor c

One can loosely speak of xor-ing together a bunch of values, but the underlying operation always takes two operands.