Difference between revisions of "And"

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(manually undo last changes by RfC1394: use categorization template {{and}} and fix syntax highlighting)
 
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{{And}}
 
{{And}}
  
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= Boolean operation =
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The binary operator <syntaxhighlight lang="pascal" inline>and</syntaxhighlight> performs a logical conjunction.
 +
[[FPC]] also does a bitwise <syntaxhighlight lang="pascal" inline>and</syntaxhighlight> when supplied with ordinal types.
  
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'''And''' produces a value of [[True|true]] if and only if both of its operands are true.
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== Boolean operation ==
 +
The operator <syntaxhighlight lang="pascal" inline>and</syntaxhighlight> accepts to two Boolean type values.
 +
It is the logical conjunction written in classic logic as <math>A \land B</math>.
 +
Electrical engineers may write <math>A \times B</math> or <math>A \cdot B</math>, or eliminating the multiplication sign altogether writing <math>AB</math>.
 +
However, the [[*|asterisk]] has a different meaning in programming.
 +
The Boolean <syntaxhighlight lang="pascal" inline>and</syntaxhighlight> evaluates to [[false and true|<syntaxhighlight lang="pascal" inline>true</syntaxhighlight>]] if and only if both operands are <syntaxhighlight lang="pascal" inline>true</syntaxhighlight>.
  
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== Truth table ==
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{| class="wikitable" style="text-align:center; margin:auto;"
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! <syntaxhighlight lang="pascal" inline>A</syntaxhighlight>
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{| border="1" style="border: 1px  solid; border-collapse: collapse;"
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! <syntaxhighlight lang="pascal" inline>B</syntaxhighlight>
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! <syntaxhighlight lang="pascal" inline>A and B</syntaxhighlight>
 
|-
 
|-
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!align=center| A !! align=center|B !! &nbsp; A and B &nbsp;
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| <syntaxhighlight lang="pascal" inline>false</syntaxhighlight>
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| <syntaxhighlight lang="pascal" inline>false</syntaxhighlight>
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| style="background: #eeeeee" | <syntaxhighlight lang="pascal" inline>false</syntaxhighlight>
 
|-
 
|-
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| &nbsp; false &nbsp;|| &nbsp; false &nbsp;
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| <syntaxhighlight lang="pascal" inline>false</syntaxhighlight>
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|style="background: #eeeeee" | &nbsp; false
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| <syntaxhighlight lang="pascal" inline>true</syntaxhighlight>
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| style="background: #eeeeee" | <syntaxhighlight lang="pascal" inline>false</syntaxhighlight>
 
|-
 
|-
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| &nbsp; false || &nbsp; true
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| <syntaxhighlight lang="pascal" inline>true</syntaxhighlight>
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|style="background: #eeeeee" | &nbsp; false
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| <syntaxhighlight lang="pascal" inline>false</syntaxhighlight>
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| style="background: #eeeeee" | <syntaxhighlight lang="pascal" inline>false</syntaxhighlight>
 
|-
 
|-
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| &nbsp; true || &nbsp; false
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| <syntaxhighlight lang="pascal" inline>true</syntaxhighlight>
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|style="background: #eeeeee" | &nbsp; false
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| <syntaxhighlight lang="pascal" inline>true</syntaxhighlight>
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|-
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| style="background: #eeeeee" | <syntaxhighlight lang="pascal" inline>true</syntaxhighlight>
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| &nbsp; true || &nbsp; true  
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|+ truth table for logical conjunction
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|style="background: #eeeeee" | &nbsp; true
 
 
|}
 
|}
  
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== Bitwise operation ==
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FPC also defines a bitwise <syntaxhighlight lang="pascal" inline>and</syntaxhighlight>.
 +
Taking two ordinal operands logical <syntaxhighlight lang="pascal" inline>and</syntaxhighlight> is calculated bit by bit:
 +
    1010'1100
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and 0011'0100
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――――――――――――
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    0010'0100
  
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= Bitwise operation =
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== comparative remarks ==
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Depending on the compiler's specific implementation of the data type [[Set|<syntaxhighlight lang="pascal" inline>set</syntaxhighlight>]], the [[Asterisk|intersection of sets]] virtually does the same as the bitwise <syntaxhighlight lang="pascal" inline>and</syntaxhighlight>.
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Bitwise and sets a bit to 1 if and only if all of the corresponding bits in its operands are 1.
 
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== Clear a bit ==
 
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<delphi>
 
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function ClearBit(const AValue, ABitNumber:integer):integer;
 
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begin
 
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  result := AValue and not(1 shl ABitNumber);
 
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end;
 
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</delphi>
 
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If you call ClearBit(%1111,1) then get %1101 (%1111 = 15 and %1101 = 13). If you call ClearBit(13,2) then get 9 (9 = %1001) .
 
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=== Read more ===
 
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* [[Not]]
 
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* [[Shl]]
 
  
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* [[Const]]
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== see also ==
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* [[Function]]
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* [[Or|<syntaxhighlight lang="pascal" inline>or</syntaxhighlight>]]
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* [[Integer]]
 

Latest revision as of 15:57, 27 November 2022

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The binary operator and performs a logical conjunction. FPC also does a bitwise and when supplied with ordinal types.

Boolean operation

The operator and accepts to two Boolean type values. It is the logical conjunction written in classic logic as [math]\displaystyle{ A \land B }[/math]. Electrical engineers may write [math]\displaystyle{ A \times B }[/math] or [math]\displaystyle{ A \cdot B }[/math], or eliminating the multiplication sign altogether writing [math]\displaystyle{ AB }[/math]. However, the asterisk has a different meaning in programming. The Boolean and evaluates to true if and only if both operands are true.

A B A and B
false false false
false true false
true false false
true true true
truth table for logical conjunction

Bitwise operation

FPC also defines a bitwise and. Taking two ordinal operands logical and is calculated bit by bit: 

    1010'1100
and 0011'0100
――――――――――――
    0010'0100

comparative remarks

Depending on the compiler's specific implementation of the data type set, the intersection of sets virtually does the same as the bitwise and.

see also

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