Binary bitwise operators in JavaScript

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, n_i 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: result_i = number1_i && number2_i
  


• Or: result_i = number1_i || number2_i
  


• Xor: result_i = number1_i ^^ number2_i
  

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