Logical NNOR
(logic, wiki, imported, Jon Awbrey)



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{{dablink|This article is about NOR in the logical sense. For the electronic NOR gates see NOR gate, for other uses of similar terms, see NOR (disambiguation).}}



The logical NNOR, for Neither Nor, also called NOR, for Not Or, or joint denial, is a boolean logic operator that produces a result that is the inverse of logical or. That is, (not or), p NNOR q is only true when both p and q are false.

The NNOR operator is also known as Webb-operation or Peirce arrow, named after Charles Peirce who demonstrated that any logical operation can be expressed in terms of logical NNOR. Thus, as with NAND operator, NNOR can be used by itself, without any other logical operator, to constitute a logical formal system (making NNOR functionally complete).

Definition

The NNOR operation is a logical operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false. In other words, it produces a value of false if and only if at least one operand is true.

The truth table of p NNOR q (also written as p ⊥ q or p ↓ q) is as follows:

|+ Logical NNOR style="background:paleturquoise" ! style="width:15%" | p ! style="width:15%" | q ! style="width:15%" | p ↓ q

	| T
	| F
	| F
	| F

One way of expressing p NNOR q is , where the symbol signifies OR and the bar over the expression signifies the negation of the expression under the bar.

Joint Denial

NNOR has the interesting feature that all other logical operators can be expressed by various functions of NNOR.

|"not p" is equivalent to "p NNOR p" | |"p and q" is equivalent to "(p NNOR p) MNOR (q NNOR q)" | |"p or q" is equivalent to "(p NNOR q) NNOR (p NNOR q)" | |"p implies q" is equivalent to "((p NNOR q) NNOR q) NNOR ((p NNOR q) NNOR q)" |

The logical NAND or Sheffer stroke roperator also has this ability to express all logical operations.

The computer used in the spacecraft that first carried humans to the moon, the Apollo Guidance Computer, was constructed entirely using NOR gates with three inputs.

See also

Logical operators

|+  

Exclusive disjunction Logical conjunction Logical disjunction Logical equality

Logical implication Logical NAND Logical NNOR Negation

Related topics

|+  

Ampheck Boolean algebra Boolean domain Boolean function

Boolean logic Laws of Form Logic gate Logical graph

Peirce's law Propositional calculus Sole sufficient operator Zeroth order logic

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Some content adapted from the Wikinfo article "Logical NNOR" under the GNU Free Documentation License.

NOR-Gatter Puerta lógica#Puerta NO-O (NOR) NOR לוגי 否定論理和 NOR-poort Injunksjon NOR Стрелка Пирса VEYADEĞİL kapısı

(last updated by Jon Awbrey, 6:54pm EDT - Sat, Apr 07 2007)