In Boolean logic, logical NOR or non-disjunction or joint denial 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 of p and q are false. It is logically equivalent to and , where the symbol signifies logical negation, signifies OR, and signifies AND. 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. The NOR 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 is as follows: The logical NOR is the negation of the disjunction: Peirce is the first to show the functional completeness of non-disjunction while he doesn't publish his result. Peirce used for non-conjunction and for non-disjunction (in fact, what Peirce himself used is and he didn't introduce while Peirce's editors made such disambiguated use). Peirce called as (from Ancient Greek ἀμφήκης, amphēkēs, "cutting both ways"). In 1911, Stamm was the first to publish a description of both non-conjunction (using , the Stamm hook), and non-disjunction (using , the Stamm star), and showed their functional completeness. Note that most uses in logical notation of use this for negation. In 1913, Sheffer described non-disjunction and showed its functional completeness. Sheffer used for non-conjunction, and for non-disjunction. In 1935, Webb described non-disjunction for -valued logic, and use for the operator.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related courses (5)
EE-110: Logic systems (for MT)
Ce cours couvre les fondements des systèmes numériques. Sur la base d'algèbre Booléenne et de circuitscombinatoires et séquentiels incluant les machines d'états finis, les methodes d'analyse et de syn
EE-207: Logic systems (for EL)
Ce cours couvre les fondements des systèmes numériques. Sur la base d'algèbre Booléenne et de circuits combinatoires et séquentiels incluant les machines d'états finis, les methodes d'analyse et de sy
CS-101: Advanced information, computation, communication I
Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics a
Show more
Related lectures (33)
Common Multiplicand Speedup
Explores common multiplicand speedup through logical operations like bitwise AND and XOR to optimize the multiplication process.
System-R Optimizer: Query Optimization and Cost Estimation
Explores the System-R Optimizer, query optimization, cost estimation, join orderings, and cardinality challenges in database systems.
Matlab: 3D Surface Plotting
Covers logical arrays, 3D surface plotting, parametric curves, interpolation, and fitting in Matlab.
Show more
Related publications (21)

Programmable Seizure Detector Using a 32-bit RISC Processor for Implantable Medical Devices

Alexandre Schmid, Keyvan Farhang Razi

A programmable patient-customized epileptic seizure detector is proposed in this paper to enable neurologists and patients to have constructive interactions with the implantable medical device. The programmability feature is enabled by designing a low-powe ...
IEEE2023

Programmable Logic Gates Based On Tunable Multistable Mechanisms

Simon Nessim Henein, Hubert Pierre-Marie Benoît Schneegans, Ilan Vardi, Mohamed Gamal Abdelrahman Ahmed Zanaty

Binary logic operations are the building blocks of computing machines. In this paper, we present a new programmable binary logic gate based on programmable multistable mechanisms (PMM), which are multistable structures whose stability behavior depends on m ...
AMER SOC MECHANICAL ENGINEERS2020

Reconfigurable Logic Gates Based on Programable Multistable Mechanisms

Simon Nessim Henein, Hubert Pierre-Marie Benoît Schneegans, Ilan Vardi, Mohamed Gamal Abdelrahman Ahmed Zanaty

Binary logic gates are building blocks of computing machines, in particular, electronic computers. One variant is the programable logic gate, also known as the reconfigurable logic gate, in which the logical function implemented can be modified. In this pa ...
ASME2020
Show more
Related people (1)
Related concepts (16)
Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid.
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬.
Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form , where is known as the Boolean domain and is a non-negative integer called the arity of the function.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.