Difference between revisions of "And"

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(→‎Bitwise operation: mention operands need to be ordinal and it is referred to as a "logical and" in the documentation.)
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{{And}}
 
{{And}}
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 +
The binary operator {{HL|and}} performs a logical conjunction.
 +
[[FPC]] also does a bitwise {{HL|and}} when supplied with ordinal types.
  
 
== Boolean operation ==
 
== Boolean operation ==
 +
The operator {{HL|and}} 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 {{HL|and}} evaluates to [[false and true|{{HL|true}}]] if and only if both operands are {{HL|true}}.
  
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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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{| class="wikitable" style="text-align:center; margin:auto;"
−
 
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! {{HL|A}}
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=== Truth table ===
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! {{HL|B}}
−
 
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! {{HL|A and B}}
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{| class="wikitable"
 
 
|-
 
|-
−
! A !! B !! A and B
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| {{HL|false}}
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| {{HL|false}}
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| style="background: #eeeeee" | {{HL|false}}
 
|-
 
|-
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| &nbsp; false &nbsp;|| &nbsp; false &nbsp;
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| {{HL|false}}
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|style="background: #eeeeee" | &nbsp; false
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| {{HL|true}}
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| style="background: #eeeeee" | {{HL|false}}
 
|-
 
|-
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| &nbsp; false || &nbsp; true
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| {{HL|true}}
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|style="background: #eeeeee" | &nbsp; false
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| {{HL|false}}
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| style="background: #eeeeee" | {{HL|false}}
 
|-
 
|-
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| &nbsp; true || &nbsp; false
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| {{HL|true}}
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|style="background: #eeeeee" | &nbsp; false
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| {{HL|true}}
−
|-
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| style="background: #eeeeee" | {{HL|true}}
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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
 
 
|}
 
|}
−
 
  
 
== Bitwise operation ==
 
== Bitwise operation ==
 +
FPC also defines a bitwise <syntaxhighlight lang="pascal" enclose="none">and</syntaxhighlight>.
 +
Taking two ordinal operands logical <syntaxhighlight lang="pascal" enclose="none">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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Logical '''And''' (aka Bitwise And) requires ordinal operands and sets a bit in the result variable to 1 if and only if both of the corresponding bits in the operands are 1.
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== comparative remarks ==
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Depending on the compiler's specific implementation of the data type [[Set|{{HL|set}}]], the [[Asterisk|intersection of sets]] virtually does the same as the bitwise {{HL|and}}.
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=== Is power of two ===
 
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<syntaxhighlight>
 
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function IsPowerOfTwo( const aValue : longint ): boolean;
 
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var
 
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  x : longint;
 
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  b : boolean;
 
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begin
 
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  b := false;
 
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  if aValue <> 0 then
 
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    begin
 
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      x := aValue - 1;
 
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      x := x and aValue;
 
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      if x = 0 then b := true;
 
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    end;
 
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  result := b;
 
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end; 
 
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</syntaxhighlight>
 
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If you call IsPowerOfTwo(4) then you get true. If you call IsPowerOfTwo(5) then you get false .
 
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== See also ==
 
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* [[Not]]
 
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* [[Or]]
 
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* [[Shl]]
 
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* [[Const]]
 
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* [[Function]]
 
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* [[Integer]]
 
  
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* [[Shl# Clear a bit|Clear a bit]]
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{{Logical operators}}
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* [[Bit manipulation]]
 
  
 
[[Category:Pascal]]
 
[[Category:Pascal]]
 +
[[Category:Operators]]

Revision as of 21:13, 29 August 2021

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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.


navigation bar: Pascal logical operators
operators

and • or • not • xor
shl • shr
and_then (N/A)• or_else (N/A)

see also

{$boolEval} • Reference: § “boolean operators” • Reference: § “logical operators”

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