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Xor

XOR stands for exclusive-or, a less familiar operation unless you are already a seasoned programmer or logician.

XOR is usually denoted by the symbol ⊕. \( x \oplus y \) is True only if just one of \( x \) and \( y \) is True. Its table is like the ADD table, but with a different twist than with OR. 

    ⊕|  0   1
  ---+-------
    0|  0   1
    1|  1   0

XOR applied to two bytes is applied bit by bit.

Example

Here is the XOR of two data bytes. 

      01100100
    ⊕ 00111101
  ------------
      01011001

If the usefulness of XOR isn't obvious, we can define binary addition in terms of logical operations. 


     x
   + y
  ----
    ab   a = x ∧ y
         b = x ⊕ y
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