JavaScript Bitwise Operations

JavaScript Bitwise Operators

Operator Name Description
& AND Sets each bit to 1 if both bits are 1
| OR Sets each bit to 1 if one of two bits is 1
^ XOR Sets each bit to 1 if only one of two bits is 1
~ NOT Inverts all the bits
<< Zero fill left shift Shifts left by pushing zeros in from the right and let the leftmost bits fall off
>> Signed right shift Shifts right by pushing copies of the leftmost bit in from the left, and let the rightmost bits fall off
>>> Zero fill right shift Shifts right by pushing zeros in from the left, and let the rightmost bits fall off

Examples

Operation Result Same as Result
5 & 1 1 0101 & 0001  0001
5 | 1 5 0101 | 0001  0101
~ 5 10  ~0101  1010
5 << 1 10 0101 << 1  1010
5 ^ 1 4 0101 ^ 0001  0100
5 >> 1 2 0101 >> 1  0010
5 >>> 1 2 0101 >>> 1  0010

JavaScript Uses 32 bits Bitwise Operands

JavaScript stores numbers as 64 bits floating point numbers, but all bitwise operations are performed on 32 bits binary numbers.

Before a bitwise operation is performed, JavaScript converts numbers to 32 bits signed integers.

After the bitwise operation is performed, the result is converted back to 64 bits JavaScript numbers.

The examples above uses 4 bits unsigned binary numbers. Because of this ~ 5 returns 10.

Since JavaScript uses 32 bits signed integers, it will not return 10. It will return -6.

00000000000000000000000000000101 (5)

11111111111111111111111111111010 (~5 = -6)

A signed integer uses the leftmost bit as the minus sign.

Bitwise AND

When a bitwise AND is performed on a pair of bits, it returns 1 if both bits are 1.

One bit example:

Operation Result
0 & 0 0
0 & 1 0
1 & 0 0
1 & 1 1

4 bits example:

Operation Result
1111 & 0000 0000
1111 & 0001 0001
1111 & 0010 0010
1111 & 0100 0100

Bitwise OR

When a bitwise OR is performed on a pair of bits, it returns 1 if one of the bits are 1:

One bit example:

Operation Result
0 | 0 0
0 | 1 1
1 | 0 1
1 | 1 1

4 bits example:

Operation Result
1111 | 0000 1111
1111 | 0001 1111
1111 | 0010 1111
1111 | 0100 1111

Bitwise XOR

When a bitwise XOR is performed on a pair of bits, it returns 1 if the bits are different:

One bit example:

Operation Result
0 ^ 0 0
0 ^ 1 1
1 ^ 0 1
1 ^ 1 0

4 bits example:

Operation Result
1111 ^ 0000 1111
1111 ^ 0001 1110
1111 ^ 0010 1101
1111 ^ 0100 1011

JavaScript Bitwise AND (&)

Bitwise AND returns 1 only if both bits are 1:

Decimal Binary
5 00000000000000000000000000000101
1 00000000000000000000000000000001
5 & 1 00000000000000000000000000000001 (1)

Example

var x = 5 & 1;

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JavaScript Bitwise OR (|)

Bitwise or returns 1 if one of the bits are 1:

Decimal Binary
5 00000000000000000000000000000101
1 00000000000000000000000000000001
5 | 1 00000000000000000000000000000101 (5)

Example

var x = 5 | 1;

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JavaScript Bitwise XOR (^)

Bitwise XOR returns 1 if the bits are different:

Decimal Binary
5 00000000000000000000000000000101
1 00000000000000000000000000000001
5 ^ 1 00000000000000000000000000000100 (4)

Example

var x = 5 ^ 1;

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JavaScript Bitwise NOT (~)

Decimal Binary
5 00000000000000000000000000000101
~5 11111111111111111111111111111010 (-6)

Example

var x = ~5;

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JavaScript (Zero Fill) Bitwise Left Shift (<<)

This is a zero fill left shift. One or more zero bits are pushed in from the right, and the leftmost bits fall off:

Decimal Binary
5 00000000000000000000000000000101
5 << 1 00000000000000000000000000001010 (10)

Example

var x = 5 << 1;

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JavaScript (Sign Preserving) Bitwise Right Shift (>>)

This is a sign preserving right shift. Copies of the leftmost bit are pushed in from the left, and the rightmost bits fall off:

Decimal Binary
-5 11111111111111111111111111111011
-5 >> 1 11111111111111111111111111111101 (-3)

Example

var x = -5 >> 1;

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JavaScript (Zero Fill) Right Shift (>>>)

This is a zero fill right shift. One or more zero bits are pushed in from the left, and the rightmost bits fall off:

Decimal Binary
5 00000000000000000000000000000101
5 >>> 1 00000000000000000000000000000010 (2)

Example

var x = 5 >>> 1;

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Binary Numbers

Binary numbers with only one bit set is easy to understand:

Binary Representation Decimal value
00000000000000000000000000000001 1
00000000000000000000000000000010 2
00000000000000000000000000000100 4
00000000000000000000000000001000 8
00000000000000000000000000010000 16
00000000000000000000000000100000 32
00000000000000000000000001000000 64

Setting a few more bits reveals the binary pattern:

Binary Representation Decimal value
00000000000000000000000000000101 5 (4 + 1)
00000000000000000000000000001101 13 (8 + 4 + 1)
00000000000000000000000000101101 45 (32 + 8 + 4 + 1)

JavaScript binary numbers are stored in two’s complement format.

This means that a negative number is the bitwise NOT of the number plus 1:

Binary Representation Decimal value
00000000000000000000000000000101 5
11111111111111111111111111111011 -5
00000000000000000000000000000110 6
11111111111111111111111111111010 -6
00000000000000000000000000101000 40
11111111111111111111111111011000 -40

Converting Decimal to Binary

Example

function dec2bin(dec){
return (dec >>> 0).toString(2);
}

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Converting Binary to Decimal

Example

function bin2dec(bin){
return parseInt(bin, 2).toString(10);
}

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