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Logical NOR
Binary operation that is true if and only if both operands are false / From Wikipedia, the free encyclopedia
In Boolean logic, logical NOR,[1] non-disjunction, or joint denial[1] is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false. It is logically equivalent to and
, where the symbol
signifies logical negation,
signifies OR, and
signifies AND.
NOR | |
---|---|
![]() | |
Definition | |
Truth table | |
Logic gate | ![]() |
Normal forms | |
Disjunctive | |
Conjunctive | |
Zhegalkin polynomial | |
Post's lattices | |
0-preserving | no |
1-preserving | no |
Monotone | no |
Affine | no |
Self-dual | no |
Non-disjunction is usually denoted as or
or
(prefix) or
.
As with its dual, the NAND operator (also known as the Sheffer stroke—symbolized as either ,
or
), NOR can be used by itself, without any other logical operator, to constitute a logical formal system (making NOR functionally complete).
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.[2]