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7.5 JS Bitwise

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 1: JS Bitwise AND

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 2: JS Bitwise OR

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 3: JS Bitwise XOR

var x = 5 ^ 1;

JavaScript Bitwise NOT (~)

Decimal	Binary
5	00000000000000000000000000000101
˜5	11111111111111111111111111111010 (-6)

Example 4: JS Bitwise NOT

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 5: JS Bitwise Left

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 6: JS Bitwise Right

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 7: JS Unsigned Bitwise Right

var x = 5 >>> 1;

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 8: JS Convert Decimal to Binary

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

Converting Binary to Decimal

Example 9: JS Convert Binary to Decimal

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

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