Binary bitwise operators in JavaScript

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This blog post describes JavaScript’s binary bitwise operators: bitwise And (&), bitwise Or (|), and bitwise Xor (^).


These operators work with 32-bit integers. That is, they convert their operands to 32-bit integers and produce a result that is a 32-bit integer (encoded as a floating point number, at least externally).

Inputting and outputting binary numbers



In the following examples, we work with binary numbers, via the following two operations:


parseInt(str, 2) parses a string str in binary notation (base 2). For example:


    > parseInt('110', 2)
    6


num.toString(2) converts the number num to a string in binary notation. For example:


    > 6..toString(2)
    '110'


Binary bitwise operators



Bitwise And: number1 & number2

    > (parseInt('11001010', 2) & parseInt('1111', 2)).toString(2)
    '1010'


Bitwise Or: number1 | number2

    > (parseInt('11001010', 2) | parseInt('1111', 2)).toString(2)
    '11001111'


Bitwise Xor (eXclusive Or): number1 ^ number2

    > (parseInt('11001010', 2) ^ parseInt('1111', 2)).toString(2)
    '11000101'


There are two ways to intuitively understand binary bitwise operators.


First explanation: one boolean operation per bit. In the formulas below, ni means bit i of number n interpreted as a boolean (0 is false, 1 is true). For example, 20 is false, 21 is true.


  • And: resulti = number1i && number2i

  • Or: resulti = number1i || number2i

  • Xor: resulti = number1i ^^ number2i


The operator ^^ does not exist. If it did, it would work like this (the result is true if exactly one of the operands is true):

    x ^^ y === (x && !y) || (!x && y)


Second explanation: changing bits of number1 via number2.


  • And: keeps only those bits of number1 that are set in number2. This operation is also called masking, with number2 being the mask.

  • Or: sets all bits of number1 that are set in number2 and keeps all other bits unchanged.

  • Xor: inverts all bits of number1 that are set in number2 and keeps all other bits unchanged.



Further reading




  1. Integers and shift operators in JavaScript

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