## More on XOR

I didn t realize it until I typed the title but it rhymed. (I m poet and I don t even know it!)  I have researched and thought more about XOR.  And decided that the definition of XOR. is was it is.  Here is how I explained it in a new book I am writing.

Sometimes people get things wrong but the name sticks because no one wants to make the effort to change back.  XOR stands for exclusive OR and its output should be 1 only when a single input is 1.  Its algebraic operator is ^ .  It was originally defined as a two input gate and functioned very well in that form.  The problem is for more than two inputs it is no longer associative ((A ^ B ^ C) (A ^ B) ^ C.  So the definition was changed to define the output as 1 when an odd number of its inputs are 1.  It really should be called an ODD gate but then again a Koala shouldn t be called a bear or a tomato a vegetable. A peanut is neither a pea nor a nut and we won t even go into sweetbreads.  Just get over it.

Identities           0 ^0 = 0

1 ^ 1 = 0

1 ^ 0 = 1

A^ 1 = ~ A

A ^ 0 = A

A ^ A= 0

A ^ ~A= 1

(A ^ B ^ C) = (A ^ B) ^| C (associative)

A ^B= B ^ A (commutative)

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