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NAND
NAND, also known as the Sheffer stroke, is aconnective inlogic equivalent to the compositionNOTAND that yieldstrue if any condition isfalse, andfalse if all conditions aretrue.
NAND
is equivalent to
, where
denotesNOT and
denotesAND. Inpropositional calculus, the termalternative denial is used to refer to the NAND connective. Notations for NAND include
and
(Mendelson 1997, p. 26). The NAND operation is implemented asNand[A,B, ...]. The circuit diagram symbol for an NAND gate is illustrated above.
Thebinary NAND operator has the followingtruth table (Mendelson 1997, p. 27).
 |  |  |
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | T |
The NAND operation is the basic logical operation performed by the solid-state transistors ("NAND gates") that underlie virtually all integrated circuits and modern computers. The first axiom system based on NAND was given by Henry Sheffer in 1913. In their landmark tome, Whitehead and Russell (1927) promoted NAND as the appropriate foundation for axiomatic logic.
TheAND function
can be written in terms of NANDs as
 |
See also
AND,Binary Operator,Connective,Intersection,NOR,NOT,OR,Truth Table,XNOR,XORExplore with Wolfram|Alpha
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References
Mendelson, E.Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.Simpson, R. E. "The NAND Gate." §12.5.5 inIntroductory Electronics for Scientists and Engineers, 2nd ed. Boston, MA: Allyn and Bacon, pp. 548-550, 1987.Whitehead, A. N. and Russell, B.Principia Mathematica. New York: Cambridge University Press, 1927.Referenced on Wolfram|Alpha
NANDCite this as:
Weisstein, Eric W. "NAND." FromMathWorld--AWolfram Resource.https://mathworld.wolfram.com/NAND.html