The operation yields the result TRUE when one, and only one, of its operands is TRUE.
For two inputs A and B, the truth table of the function is as follows.
A B | A xor B ----+-------- F F | F F T | T T F | T T T | FIt can be deduced from this table that
- (A xor B) = (A and not B) or (not A and B) = (A or B) and (not A or not B) = (A or B) and not (A and B)
- a plus sign ("+") or a plus sign that is modified in some way, such as being put inside a circle ("⊕"); this is used because exclusive disjunction corresponds to addition modulo 2 if F = 0 and T = 1.
- a vee that is modified in some way, such as being underlined ("∨"); this is used because exclusive disjunction is a modification of ordinary (inclusive) disjunction, which is typically denoted by a vee.
- a caret ("^"), as in the C programming language
Binary values xor'ed by themselves are always zero. In some computer architectures, it is faster to store a zero in a register by xor'ing the value with itself instead of loading and storing the value zero. Thus, on some computer architectures, xor'ing values with themselves is a common optimization.
See also: Symmetric difference, or, and, Xor swap algorithm, Xor linked list