What are XAND and XOR

Question

What are XAND and XOR? Also is there an XNot

Answer 1

There's a simple argument to see where the binary logic gates come from, using truth tables, which have come up already.

There are six that represent commutative operations, in which a op b == b op a. Each binary operator has an associated three column truth table that defines it. The first two columns can be fixed for the defining tables for all the operators.

Consider the third column. It's a sequence of four binary digits. There are sixteen combinations, but the constraint of commutativity effectively removes one row from the truth tables, so it's only eight. Two more get knocked off because all truths or all falses isn't a useful gate. These are the familiar or, and, and xor, plus their negations.