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The symbol used for exclusive disjunction varies from one field of application to the next, and even depends on the properties being emphasized in a given context of discussion. In addition to the abbreviation "XOR", any of the following symbols may also be seen: + was used by George Boole in 1847. [6]
XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or from mathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
In cryptography, the simple XOR cipher is a type of additive cipher, [1] an encryption algorithm that operates according to the principles: A ⊕ {\displaystyle \oplus } 0 = A, A ⊕ {\displaystyle \oplus } A = 0,
Disjunction: the symbol appeared in Russell in 1908 [5] (compare to Peano's use of the set-theoretic notation of union); the symbol + is also used, in spite of the ambiguity coming from the fact that the + of ordinary elementary algebra is an exclusive or when interpreted logically in a two-element ring; punctually in the history a + together ...
The Miscellaneous Mathematical Symbols-B block (U+2980–U+29FF) contains miscellaneous mathematical symbols, including brackets, angles, and circle symbols. Miscellaneous Mathematical Symbols-B [1] Official Unicode Consortium code chart (PDF)
The behavior of OR is the same as XOR except in the case of a 1 for both inputs. In situations where this never arises (for example, in a full-adder ) the two types of gates are interchangeable. This substitution is convenient when a circuit is being implemented using simple integrated circuit chips which contain only one gate type per chip.
Parity only depends on the number of ones and is therefore a symmetric Boolean function.. The n-variable parity function and its negation are the only Boolean functions for which all disjunctive normal forms have the maximal number of 2 n − 1 monomials of length n and all conjunctive normal forms have the maximal number of 2 n − 1 clauses of length n.