Yep, I shortened the notation a bit.
From Wikpedia:
Exclusive disjunction is often used for bitwise operations. Examples:
- 1 xor 1 = 0
- 1 xor 0 = 1
- 1110 xor 1001 = 0111 (this is equivalent to addition without carry)
As noted above, since exclusive disjunction is identical to addition modulo 2, the bitwise exclusive disjunction of two n-bit strings is identical to the standard vector of addition in the vector space 
.
In computer science, exclusive disjunction has several uses:
- It tells whether two bits are unequal.
- It is an optional bit-flipper (the deciding input chooses whether to invert the data input).
- It tells whether there is an odd number of 1 bits (
is true iff an odd number of the variables are true).
In logical circuits, a simple adder can be made with an XOR gate to add the numbers, and a series of AND, OR and NOT gates to create the carry output.
On some computer architectures, it is more efficient to store a zero in a register by xor-ing the register with itself (bits xor-ed with themselves are always zero) instead of loading and storing the value zero.
In simple threshold activated neural networks, modeling the ‘xor’ function requires a second layer because ‘xor’ is not a linearly-separable function.
Exclusive-or is sometimes used as a simple mixing function in cryptography, for example, with one-time pad or Feistel network systems.
XOR is used in RAID 3–6 for creating parity information. For example, RAID can “back up” bytes 10011100 and 01101100 from two (or more) hard drives by XORing (11110000) and writing to another drive. Under this method, if any one of the three hard drives are lost, the lost byte can be re-created by XORing bytes from the remaining drives. If the drive containing 01101100 is lost, 10011100 and 11110000 can be XORed to recover the lost byte.
This explanation agrees with my (educated) guess...
