22-502: (Redirected from NAND ) [REDACTED] Look up NAND in Wiktionary, the free dictionary. Nand or NAND may refer to: Computing [ edit ] Logical NAND or nand, a binary operation in logic (Not AND) NAND gate , an electronic gate that implements a logical NAND NAND logic , methods of building other logic gates using just NAND gates NAND flash memory ,
44-610: A logical NAND NAND logic , methods of building other logic gates using just NAND gates NAND flash memory , a type of non-volatile computer memory People [ edit ] Nand Kishore (cricketer, born 1970) , Indian former cricketer Nand Kishore Garg (born 1949), senior social worker Nand Gopal Gupta (born 1974), former Minister of Homeopathy in the Government of Uttar Pradesh Nainendra Nand , Solicitor-General of Fiji from 1997 to 2006 Nand Kumar Patel (1953–2013), Indian National Congress politician from
66-467: A special sign for it. It was Jean Nicod who first used the stroke as a sign for non-conjunction (NAND) in a paper of 1917 and which has since become current practice. Russell and Whitehead used the Sheffer stroke in the 1927 second edition of Principia Mathematica and suggested it as a replacement for the "OR" and "NOT" operations of the first edition. Charles Sanders Peirce (1880) had discovered
88-464: A standard formulation thereof by Huntington employing the familiar operators of propositional logic ( AND , OR , NOT ). Because of self- duality of Boolean algebras, Sheffer's axioms are equally valid for either of the NAND or NOR operations in place of the stroke. Sheffer interpreted the stroke as a sign for nondisjunction ( NOR ) in his paper, mentioning non-conjunction only in a footnote and without
110-433: A type of non-volatile computer memory People [ edit ] Nand Kishore (cricketer, born 1970) , Indian former cricketer Nand Kishore Garg (born 1949), senior social worker Nand Gopal Gupta (born 1974), former Minister of Homeopathy in the Government of Uttar Pradesh Nainendra Nand , Solicitor-General of Fiji from 1997 to 2006 Nand Kumar Patel (1953–2013), Indian National Congress politician from
132-409: Is a functionally complete set of connectives. This can be seen from the fact that NAND does not possess any of the following five properties, each of which is required to be absent from, and the absence of all of which is sufficient for, at least one member of a set of functionally complete operators: truth-preservation, falsity-preservation, linearity , monotonicity , self-duality . (An operator
154-442: Is a logical operation on two logical values . It produces a value of true, if — and only if — at least one of the propositions is false. The truth table of A ↑ B {\displaystyle A\uparrow B} is as follows. The Sheffer stroke of P {\displaystyle P} and Q {\displaystyle Q} is the negation of their conjunction By De Morgan's laws , this
176-553: Is also equivalent to the disjunction of the negations of P {\displaystyle P} and Q {\displaystyle Q} Peirce was the first to show the functional completeness of non-conjunction (representing this as ⋏ ¯ {\displaystyle {\overline {\curlywedge }}} ) but didn't publish his result. Peirce's editor added ⋏ ¯ {\displaystyle {\overline {\curlywedge }}} ) for non-disjunction . In 1911, Stamm
198-440: Is different from Wikidata All article disambiguation pages All disambiguation pages NAND (Redirected from NAND ) [REDACTED] Look up NAND in Wiktionary, the free dictionary. Nand or NAND may refer to: Computing [ edit ] Logical NAND or nand, a binary operation in logic (Not AND) NAND gate , an electronic gate that implements
220-515: Is different from Wikidata All article disambiguation pages All disambiguation pages Logical NAND In Boolean functions and propositional calculus , the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction , or alternative denial (since it says in effect that at least one of its operands
242-651: Is false), or NAND ("not and"). In digital electronics , it corresponds to the NAND gate . It is named after Henry Maurice Sheffer and written as ∣ {\displaystyle \mid } or as ↑ {\displaystyle \uparrow } or as ∧ ¯ {\displaystyle {\overline {\wedge }}} or as D p q {\displaystyle Dpq} in Polish notation by Łukasiewicz (but not as ||, often used to represent disjunction ). Its dual
SECTION 10
#1732772987076264-573: Is not clear who first introduced this notation, although the corresponding ↓ {\displaystyle \downarrow } for non-disjunction was used by Quine in 1940. The stroke is named after Henry Maurice Sheffer , who in 1913 published a paper in the Transactions of the American Mathematical Society providing an axiomatization of Boolean algebras using the stroke, and proved its equivalence to
286-500: Is the NOR operator (also known as the Peirce arrow , Quine dagger or Webb operator ). Like its dual, NAND can be used by itself, without any other logical operator, to constitute a logical formal system (making NAND functionally complete ). This property makes the NAND gate crucial to modern digital electronics , including its use in computer processor design. The non-conjunction
308-406: Is truth-functionally equivalent to ¬ ( A ∧ B ) {\displaystyle \neg (A\land B)} , and A ∨ B {\displaystyle A\lor B} is equivalent to ¬ ( ¬ A ∧ ¬ B ) {\displaystyle \neg (\neg A\land \neg B)} , the Sheffer stroke suffices to define
330-496: Is truth-preserving if its value is truth whenever all of its arguments are truth, or falsity-preserving if its value is falsity whenever all of its arguments are falsity.) It can also be proved by first showing, with a truth table , that ¬ A {\displaystyle \neg A} is truth-functionally equivalent to A ↑ A {\displaystyle A\uparrow A} . Then, since A ↑ B {\displaystyle A\uparrow B}
352-802: The functional completeness of NAND or NOR more than 30 years earlier, using the term ampheck (for 'cutting both ways'), but he never published his finding. Two years before Sheffer, Edward Stamm [ pl ] also described the NAND and NOR operators and showed that the other Boolean operations could be expressed by it. NAND is commutative but not associative, which means that P ↑ Q ↔ Q ↑ P {\displaystyle P\uparrow Q\leftrightarrow Q\uparrow P} but ( P ↑ Q ) ↑ R ↮ P ↑ ( Q ↑ R ) {\displaystyle (P\uparrow Q)\uparrow R\not \leftrightarrow P\uparrow (Q\uparrow R)} . The Sheffer stroke, taken by itself,
374-837: The Chhattisgarh Nand Singh (1914–1947), Indian recipient of the Victoria Cross Lisa Francesca Nand (born 1974), journalist Nand Lal Noorpuri (died 1966), Punjabi poet, writer and lyricist Other uses [ edit ] Nand Dam , the Lower Wunna Dam over the Nand river Nanda Baba or Nand, a figure in Hindu mythology Nand (TV series) , a Pakistani TV series produced by ARY Digital See also [ edit ] Nanda (disambiguation) Topics referred to by
396-502: The Chhattisgarh Nand Singh (1914–1947), Indian recipient of the Victoria Cross Lisa Francesca Nand (born 1974), journalist Nand Lal Noorpuri (died 1966), Punjabi poet, writer and lyricist Other uses [ edit ] Nand Dam , the Lower Wunna Dam over the Nand river Nanda Baba or Nand, a figure in Hindu mythology Nand (TV series) , a Pakistani TV series produced by ARY Digital See also [ edit ] Nanda (disambiguation) Topics referred to by
418-452: The Sheffer stroke. In 1928, Hilbert and Ackermann described non-conjunction with the operator / {\displaystyle /} . In 1929, Łukasiewicz used D {\displaystyle D} in D p q {\displaystyle Dpq} for non-conjunction in his Polish notation . An alternative notation for non-conjunction is ↑ {\displaystyle \uparrow } . It
440-459: The same term [REDACTED] This disambiguation page lists articles associated with the title Nand . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Nand&oldid=1159274138 " Categories : Disambiguation pages Disambiguation pages with surname-holder lists Hidden categories: Short description
462-459: The same term [REDACTED] This disambiguation page lists articles associated with the title Nand . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Nand&oldid=1159274138 " Categories : Disambiguation pages Disambiguation pages with surname-holder lists Hidden categories: Short description
SECTION 20
#1732772987076484-794: Was the first to publish a proof of the completeness of non-conjunction, representing this with ∼ {\displaystyle \sim } (the Stamm hook ) and non-disjunction in print at the first time and showed their functional completeness. In 1913, Sheffer described non-disjunction using ∣ {\displaystyle \mid } and showed its functional completeness. Sheffer also used ∧ {\displaystyle \wedge } for non-disjunction. Many people, beginning with Nicod in 1917, and followed by Whitehead, Russell and many others, mistakenly thought Sheffer has described non-conjunction using ∣ {\displaystyle \mid } , naming this
#75924