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→Boolean function
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== Boolean function == | == Boolean function == | ||
When the arguments to Not Equal to are [[Boolean]], it is the [[wikipedia:exclusive or|exclusive or]] or xor function | When the arguments to Not Equal to are [[Boolean]], it is the [[wikipedia:exclusive or|exclusive or]] or xor function: | ||
{|class=wikitable | |||
!<source lang=apl inline>≠</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source> | |||
|- | |||
!<source lang=apl inline>0</source> | |||
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source> | |||
|- | |||
!<source lang=apl inline>1</source> | |||
|<source lang=apl inline>1</source>||<source lang=apl inline>0</source> | |||
|} | |||
Xor is one of the most important [[Boolean function]]s because it is equivalent to [[addition]] of the arguments with [[modulus]] 2. Like addition, it is [[wikipedia:Commutative property|commutative]] and [[wikipedia:Associative property|associative]]. It is also equivalent to [[subtraction]] with modulus 2 because the [[Minus|negative]] of a number is the same as the original number (mod 2): the negative of an odd number is still odd, and the negative of an even number is still even. | |||
[[Reduction]] of a Boolean [[vector]] using Not Equal to yields 1 if there were an odd number of 1s in the argument and 0 otherwise. In APL, if <source lang=apl inline>v</source> is a Boolean vector then <source lang=apl inline>≠/v</source> {{←→}} <source lang=apl inline>2|+/v</source>. | [[Reduction]] of a Boolean [[vector]] using Not Equal to yields 1 if there were an odd number of 1s in the argument and 0 otherwise. In APL, if <source lang=apl inline>v</source> is a Boolean vector then <source lang=apl inline>≠/v</source> {{←→}} <source lang=apl inline>2|+/v</source>. | ||