Nand: Difference between revisions

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{{Built-in|Nand|⍲}} is a [[dyadic]] [[scalar function|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 [[wikipedia:Sheffer stroke|Sheffer stroke]] or alternative denial in Boolean logic. Nand is the [[not|boolean negation]] <source lang=apl inline>~</source> of the [[And]] function <source lang=apl inline>∧</source>, and so its [[glyph]] is composed from those. However, [[fonts]] vary in how they compose them; some overlaying the glyphs (∧&#x334;), and some stacking them (∧&#x303;).
{{Built-in|Nand|⍲}} is a [[dyadic]] [[scalar function|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 [[wikipedia:Sheffer stroke|Sheffer stroke]] or alternative denial in Boolean logic. Nand is the [[not|boolean negation]] <syntaxhighlight lang=apl inline>~</source> of the [[And]] function <syntaxhighlight lang=apl inline>∧</source>, and so its [[glyph]] is composed from those. However, [[fonts]] vary in how they compose them; some overlaying the glyphs (∧&#x334;), and some stacking them (∧&#x303;).


{|class=wikitable
{|class=wikitable
!<source lang=apl inline>⍲</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
!<syntaxhighlight lang=apl inline>⍲</source>!!<syntaxhighlight lang=apl inline>0</source>!!<syntaxhighlight lang=apl inline>1</source>
|-
|-
!<source lang=apl inline>0</source>
!<syntaxhighlight lang=apl inline>0</source>
|<source lang=apl inline>1</source>||<source lang=apl inline>1</source>
|<syntaxhighlight lang=apl inline>1</source>||<syntaxhighlight lang=apl inline>1</source>
|-
|-
!<source lang=apl inline>1</source>
!<syntaxhighlight lang=apl inline>1</source>
|<source lang=apl inline>1</source>||<source lang=apl inline>0</source>
|<syntaxhighlight lang=apl inline>1</source>||<syntaxhighlight lang=apl inline>0</source>
|}
|}


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


<source lang=apl>
<syntaxhighlight lang=apl>
       0 0 1 1 ⍲ 0 1 0 1
       0 0 1 1 ⍲ 0 1 0 1
1 1 1 0
1 1 1 0

Revision as of 21:10, 10 September 2022

⍲

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 <syntaxhighlight lang=apl inline>~</source> of the And function <syntaxhighlight lang=apl inline>∧</source>, and so its glyph is composed from those. However, fonts vary in how they compose them; some overlaying the glyphs (∧̴), and some stacking them (∧̃).

<syntaxhighlight lang=apl inline>⍲</source> <syntaxhighlight lang=apl inline>0</source> <syntaxhighlight lang=apl inline>1</source>
<syntaxhighlight lang=apl inline>0</source> <syntaxhighlight lang=apl inline>1</source> <syntaxhighlight lang=apl inline>1</source>
<syntaxhighlight lang=apl inline>1</source> <syntaxhighlight lang=apl inline>1</source> <syntaxhighlight lang=apl inline>0</source>

Examples

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

<syntaxhighlight lang=apl> 

     0 0 1 1 ⍲ 0 1 0 1

1 1 1 0 </source>

External links

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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