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BitXor[n1,n2,…]

gives the bitwise XOR of the integers ni.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Applications  
Properties & Relations  
Neat Examples  
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BitXor

BitXor[n1,n2,…]

gives the bitwise XOR of the integers ni.

Details

  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • BitXor[n1,n2,…] yields the integer whose binary bit representation has ones at positions where an odd number of the binary bit representations of the ni have ones.
  • For negative integers BitXor assumes a two's complement representation.
  • BitXor automatically threads over lists.

Examples

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Basic Examples  (1)

Scope  (3)

Use numbers of any size:

BitXor takes any number of arguments:

Use negative numbers:

Generalizations & Extensions  (1)

Basic symbolic simplifications are done automatically:

Applications  (4)

Make a nested pattern:

Generate a Gray code sequence [more info]:

Bitwise version of rule 60 cellular automaton:

Properties & Relations  (4)

Truth table for Xor:

BitXor is Orderless:

Even numbers of identical arguments give 0:

Neat Examples  (3)

"Munching squares" [more info]:

Wolfram Research (1999), BitXor, Wolfram Language function, https://reference.wolfram.com/language/ref/BitXor.html.

Text

Wolfram Research (1999), BitXor, Wolfram Language function, https://reference.wolfram.com/language/ref/BitXor.html.

CMS

Wolfram Language. 1999. "BitXor." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BitXor.html.

APA

Wolfram Language. (1999). BitXor. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BitXor.html

BibTeX

@misc{reference.wolfram_2025_bitxor, author="Wolfram Research", title="{BitXor}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/BitXor.html}", note=[Accessed: 14-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_bitxor, organization={Wolfram Research}, title={BitXor}, year={1999}, url={https://reference.wolfram.com/language/ref/BitXor.html}, note=[Accessed: 14-August-2025]}