Nand

From APL Wiki
Jump to navigation Jump to search

Nand () is a dyadic scalar boolean function which tests if either argument is not true: it returns 0 if both are 1 and 1 if at least one is 0. It represents the Sheffer stroke or alternative denial in Boolean logic. Nand is the boolean negation ~ of the And function , and so its glyph is composed from those. However, fonts vary in how they compose them; some overlaying the glyphs (∧̴), and some stacking them (∧̃).

0 1
0 1 1
1 1 0

Examples

The following shows all possible combinations of inputs as a Boolean function.

      0 0 1 1 ⍲ 0 1 0 1
1 1 1 0

External links

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)
Quad names Index originComparison toleranceMigration levelAtomic vector