NOR Logic Gate

The logical NOR or joint denial is a boolean logic operator which produces a result that is the inverse of logical or. That is, (not or), p NOR q is only true when neither p NOR q is true, and is false otherwise. Image File history File links NOR.jpg NOR Logic Gate File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links NOR.jpg NOR Logic Gate File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the empty set, that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values. ... OR logic gate. ...

The NOR 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 NOR. Thus, as with NAND operator, NOR can be used by itself, without any other logical operator, to constitute a logical formal system (making NOR functionally complete). Charles Sanders Peirce Charles Sanders Santiago Peirce (pronounced purse), (September 10, 1839, Cambridge, Massachusetts – April 19, 1914, Milford, Pennsylvania) was an American polymath. ... NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ... In logic, a set of logical connectives is functionally complete if all other possible connectives can be defined in terms of it. ...

Definition

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. In mathematics, a finitary boolean function is a function of the form f : Bk → B, where B = {0, 1} is a boolean domain and where k is a nonnegative integer. ... In logic and mathematics, a logical value, also called a truth value, is a value indicating to what extent a proposition is true. ... Proposition is a term used in logic to describe the content of assertions. ...

The truth table of p NOR q (also written as p ⊥ q or p ↓ q) is as follows: Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...

One way of expressing p NOR q is , where the symbol signifies OR and the bar over the expression signifies the negation of the expression under the bar.

Joint Denial

NOR has the interesting feature that all other logical operators can be expressed by various functions of NOR. In logical calculus, logical operators or logical connectors serve to connect statements into more complicated compound statements. ...

"not p" is equivalent to "p NOR p"
"p and q" is equivalent to "(p NOR p) NOR (q NOR q)"
"p or q" is equivalent to "(p NOR q) NOR (p NOR q)"
"p implies q" is equivalent to "((p NOR q) NOR q) NOR ((p NOR q) NOR q)"

The logical NAND operator also has this ability to express all logical operations. NAND Logic gate The Sheffer stroke, written |, denotes the negation of the conjunction operation. ...

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. A computer is a machine designed for manipulating data according to a list of instructions known as a program. ... Bulk composition of the moons mantle and crust estimated, weight percent Oxygen 42. ... The Apollo Guidance Computer (AGC) was the first recognizably modern embedded system, used in real-time by astronaut pilots to collect and provide flight information, and to automatically control all of the navigational functions of the Apollo spacecraft. ...

See also

Other operators

Exclusive disjunction (usual symbol XOR occasionally EOR) is a logical operator that results in true if one of the operands, but not both of them, is true. ... AND Logic Gate In mathematics, logical conjunction (usual symbol and) is a logical operator that results in false if either of the operands is false. ... OR logic gate. ... XNOR Logic Gate Symbol Logical equality is a logical operator that corresponds to equality in boolean algebra and to the logical biconditional in propositional calculus. ... In propositional calculus, or logical calculus in mathematics, the material conditional or the implies operator is a binary truth-functional logical operator yielding the form If a then c, where a and c are statement variables (to be replaced by any meaningful indicative sentence of the language). ... NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ...

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