# Binary bitwise operators in JavaScript

[2014-01-27] bitwise_ops, numbers, dev, javascript, jsint, jslang

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, `2`_{0} is `false`, `2`_{1} 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

- Integers and shift operators in JavaScript