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BitOr[n1,n2,…]

gives the bitwise OR of the integers ni.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Neat Examples  
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BitOr

BitOr[n1,n2,…]

gives the bitwise OR of the integers ni.

Details

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

Examples

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Basic Examples  (1)

Compute the bitwise OR of two numbers:

Wolfram Language code: BitOr[61, 15]

The binary representation of 63 has ones at positions where either of the binary representations of 61 and 15 has ones:

Wolfram Language code: IntegerDigits[{61, 15, 63}, 2, 6]//Column

Scope  (4)

Use numbers of any size:

Wolfram Language code: BitOr[3 ^ 100, 5 ^ 100]

BitOr takes any number of arguments:

Wolfram Language code: BitOr[3333, 5555, 7777, 9999]

Use negative numbers:

Wolfram Language code: BitOr[-2, -3]

Basic symbolic simplifications are done automatically:

Wolfram Language code: BitOr[x, y, y, x]
Wolfram Language code: BitOr[1, 2, x]

Applications  (4)

Truth table for Or:

Wolfram Language code: Grid[Outer[BitOr, {1, 0}, {1, 0}]]

Make a nested pattern:

Wolfram Language code: ArrayPlot[Table[Boole[BitOr[i, j] == i], {i, 0, 63}, {j, 0, 63}]]

This structure corresponds to the Sierpiński gasket:

Wolfram Language code: SierpinskiMesh[5]

Plot the BitXor of with :

Wolfram Language code: ListLinePlot[Table[BitOr[i, i - 1], {i, 50}]]

Plot the BitOr of with :

Wolfram Language code: ListLinePlot[Table[BitOr[i, 2i], {i, 64}]]

Plot the BitOr of with and :

Wolfram Language code: ListLinePlot[Table[BitOr[i, 2i, 3i], {i, 64}]]

Properties & Relations  (4)

-1 corresponds to having all bits on:

Wolfram Language code: BitOr[-1, 2, x]

The BitOr of any number of copies of a number with itself is that number:

Wolfram Language code: BitOr[x, x]
Wolfram Language code: BitOr[x, x, x]

BitOr automatically threads over lists:

Wolfram Language code: BitOr[5, Range[10]]

BitOr is Orderless:

Wolfram Language code: BitOr[y, x]

Neat Examples  (1)

Plotting BitOr[x,y] in the plane shows a nested pattern of squares:

Wolfram Language code: ArrayPlot[Array[BitOr, {63, 63}]]

Plotting in three dimensions reveals a fractal structure:

Wolfram Language code: Graphics3D[Table[Cuboid[{i, j, BitOr[i, j]}], {i, 31}, {j, 31}]]

This structure corresponds to the Sierpiński sponge:

Wolfram Language code: SierpinskiMesh[5, 3]
Wolfram Research (1999), BitOr, Wolfram Language function, https://reference.wolfram.com/language/ref/BitOr.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_bitor, author="Wolfram Research", title="{BitOr}", year="1999", howpublished="\url{https://reference.wolfram.com/language/ref/BitOr.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_bitor, organization={Wolfram Research}, title={BitOr}, year={1999}, url={https://reference.wolfram.com/language/ref/BitOr.html}, note=[Accessed: 12-June-2026]}