JavaScript Bitwise Operations

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JavaScript Bitwise Operations
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JavaScript Bitwise Operators
Operator Description Example Same as Result Same as
& AND 5 & 1 0101 & 0001 1 0001
| OR 5 | 1 0101 | 0001 5 0101
~ NOT ~ 5 ~0101 10 1010
^ XOR 5 ^ 1 0101 ^ 0001 4 0100
<< Zero fill left shift 5 << 1 0101 << 1 10 1010
>> Signed right shift 5 >> 1 0101 >> 1   2 0010
>>> Zero fill right shift 5 >>> 1 0101 >>> 1   2 0010
The examples above uses 4 bits unsigned examples. But JavaScript uses 64 bits signed numbers.

Because of this (in JavaScript) ~ 5 will not return 10. It will return -6.

0000000000000000000000000000000000000000000000000000000000000101

will return:

1111111111111111111111111111111111111111111111111111111111111010

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 Operations
JavaScript bitwise operations works on 32 bits signed integers.

Any number in a bitwise operation is converted into a 32 bit signed integer.

The result of a bitwise operation is converted back into a JavaScript number.

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;
»
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;
»
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;
»
JavaScript Bitwise NOT (~)
Decimal Binary
5 00000000000000000000000000000101
~5 11111111111111111111111111111010 (-6)
Example
var x = ~5;
»
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;
»
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;
»
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;
»
Signed Numbers
Signed 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 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 -6
00000000000000000000000000101000 40
11111111111111111111111111011000 -41
Converting Decimal to Binary
Example
function dec2bin(dec){
    return (dec >>> 0).toString(2);
}
»
Converting Binary to Decimal
Example
function bin2dec(bin){
    return parseInt(bin, 2).toString(10);
}
»

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