[makecheck]

The last statement in the article is technically a hardware decision (the article says: “As an extra treat, XOR can be considered an imparity function. When its input has an even number of zeros, the output is zero. Otherwise it is one.”).

While 2-input XOR behaves as “one or the other but not both”, a many-input gate is generally implemented by chaining other XORs and the chaining causes even/odd parity instead of a “must be only one” behavior [1].

[1] https://en.wikipedia.org/wiki/XOR_gate

[SonOfLilit]

It's not "just an implementation decision"[1], it's a reasonable mathematical definition: for a binary operator OP, we define it's n-parameter version whenever a OP (b OP c) == (a OP b) op c, which is true for XOR but not e.g. for XNOR (F == F) == T is F, but F == (F == T) is T.

[1] and sorry if I'm falling victim to the difficulty of interpreting tone on the internet

[jonsen]

By symmetry it must be true for XNOR also, and:

  (F == F) == T in fact is T