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I have seen no definition for XNOT, I will propose a definition:

Let it to relate to high-impedance (Z, no signal, or perhaps null valued Boolean type Object).

0xnot 0 = Z 0xnot 1 = Z 1xnot 0 = 1 1xnot 1 = 0 

A0A0

BB00

0000: 0

0001: A Nor B

0010: A Xand B

0011: not B

0100: B Xand A

0101: not A

0110: A Xor B

0111: A Nand B

1000: A and B

1001: A XNor B

1010: A

1011: B XNand A

1100: B

1101: A XNand B

1110: A or B

1111: 1

 +---+---+---+---+ If A is: | 1 | 0 | 1 | 0 | and B is: | 1 | 1 | 0 | 0 | +---+---+---+---+ Then: yields: +-----------+---+---+---+---+ | FALSE | 0 | 0 | 0 | 0 | | A NOR B | 0 | 0 | 0 | 1 | | A XAND B | 0 | 0 | 1 | 0 | | NOT B | 0 | 0 | 1 | 1 | | B XAND A | 0 | 1 | 0 | 0 | | NOT A | 0 | 1 | 0 | 1 | | A XOR B | 0 | 1 | 1 | 0 | | A NAND B | 0 | 1 | 1 | 1 | | A AND B | 1 | 0 | 0 | 0 | | A XNOR B | 1 | 0 | 0 | 1 | | A | 1 | 0 | 1 | 0 | | B XNAND A | 1 | 0 | 1 | 1 | | B | 1 | 1 | 0 | 0 | | A XNAND B | 1 | 1 | 0 | 1 | | A OR B | 1 | 1 | 1 | 0 | | TRUE | 1 | 1 | 1 | 1 | +-----------+---+---+---+---+ 

Henceforth, the normal two-input XAND defined as

A XAND B = A AND NOT B

The complement is XNAND:

A XNAND B = B OR NOT A

A nice result from this definition is that any dual-input binary function can be expressed concisely using no more than one logical function or gate.

A0A0

BB00

0000: 0

0001: A Nor B

0010: A Xand B

0011: not B

0100: B Xand A

0101: not A

0110: A Xor B

0111: A Nand B

1000: A and B

1001: A XNor B

1010: A

1011: B XNand A

1100: B

1101: A XNand B

1110: A or B

1111: 1

Note that XAND and XNAND lack reflexivity.

This definition is extensible if we add numbered kinds of exclusive-ANDs to correspond to their corresponding minterms. Then XAND must have ceil(lg(n)) or more inputs, with the unused msbs all zeroes. The normal kind of XAND is written without a number unless used in the context of other kinds.

The various kinds of xand or xnand gates are useful for decoding.

The XOR definition is well known to be the odd-parity function. For two inputs:

A XOR B = (A AND NOT B) OR (B AND NOT A)

The complement of XOR is XNOR

A XNOR B = (A AND B) OR (NOT A AND NOT B)

Henceforth, the normal two-input XAND defined as

A XAND B = A AND NOT B

The complement is XNAND:

A XNAND B = B OR NOT A

A nice result from this XAND definition is that any dual-input binary function can be expressed concisely using no more than one logical function or gate.

A0A0

BB00

0000: 0

0001: A Nor B

0010: A Xand B

0011: not B

0100: B Xand A

0101: not A

0110: A Xor B

0111: A Nand B

1000: A and B

1001: A XNor B

1010: A

1011: B XNand A

1100: B

1101: A XNand B

1110: A or B

1111: 1

Note that XAND and XNAND lack reflexivity.

This XNAND definition is extensible if we add numbered kinds of exclusive-ANDs to correspond to their corresponding minterms. Then XAND must have ceil(lg(n)) or more inputs, with the unused msbs all zeroes. The normal kind of XAND is written without a number unless used in the context of other kinds.

The various kinds of XAND or XNAND gates are useful for decoding.

XOR is also extensible to any number of bits. The result is one if the number of ones is odd, and zero if even. If you complement any input or output bit of an XOR, the function becomes XNOR, and vice versa.