Flash cards
Review the key moves
What is the main idea behind JavaScript Bitwise Operations?
Lesson checks
Practice each idea before moving on
Short Mimo-style checks built from this lesson's code, terms, and sequence.
Which statement best captures the main point of this lesson?
Complete the missing token from the example code.
___ x = 5 & 1;Put the learning moves in the order that makes the concept easiest to apply.
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 |
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.
JavaScript Bitwise AND
When a bitwise AND is performed on a pair of bits, it returns 1 if both bits are 1.
| Operation | Result |
|---|---|
| 0 & 0 | 0 |
| 0 & 1 | 0 |
| 1 & 0 | 0 |
| 1 & 1 | 1 |
| Operation | Result |
|---|---|
| 1111 & 0000 | 0000 |
| 1111 & 0001 | 0001 |
| 1111 & 0010 | 0010 |
| 1111 & 0100 | 0100 |
JavaScript Bitwise OR
When a bitwise OR is performed on a pair of bits, it returns 1 if one of the bits is 1:
| Operation | Result | |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
| Operation | Result | |
|---|---|---|
| 1111 | 0000 | 1111 |
| 1111 | 0001 | 1111 |
| 1111 | 0010 | 1111 |
| 1111 | 0100 | 1111 |
JavaScript Bitwise XOR
When a bitwise XOR is performed on a pair of bits, it returns 1 if the bits are different:
| Operation | Result |
|---|---|
| 0 ^ 0 | 0 |
| 0 ^ 1 | 1 |
| 1 ^ 0 | 1 |
| 1 ^ 1 | 0 |
| 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
let x = 5 & 1;JavaScript Bitwise OR (|)
Bitwise OR returns 1 if one of the bits is 1:
| Decimal | Binary | |
|---|---|---|
| 5 | 00000000000000000000000000000101 | |
| 1 | 00000000000000000000000000000001 | |
| 5 | 1 | 00000000000000000000000000000101 (5) |
Example
let 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
let x = 5 ^ 1;JavaScript Bitwise NOT (~)
| Decimal | Binary |
|---|---|
| 5 | 00000000000000000000000000000101 |
| ~5 | 11111111111111111111111111111010 (-6) |
Example
let 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
let 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
let 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
let x = 5 >>> 1;Shift Assignment Operators
| Operator | Example | Same As |
|---|---|---|
| <<= | x <<= y | x = x << y |
| >>= | x >>= y | x = x >> y |
| >>>= | x >>>= y | x = x >>> y |
The <<= Operator
The Left Shift Assignment Operator left shifts a variable.
Left Shift Assignment Example
let x = -100;
x <<= 5;The >>= Operator
The Right Shift Assignment Operator right shifts a variable (signed).
Right Shift Assignment Example
let x = -100;
x >>= 5;The >>>= Operator
The Unsigned Right Shift Assignment Operator right shifts a variable (unsigned).
Unsigned Right Shift Assignment Example
let x = -100;
x >>>= 5;Bitwise Assignment Operators
| Operator | Example | Same As | ||
|---|---|---|---|---|
| &= | x &= y | x = x & y | ||
| ^= | x ^= y | x = x ^ y | ||
| = | x | = y | x = x | y |
The &= Operator
The Bitwise AND Assignment Operator does a bitwise AND operation on two operands and assigns the result to the the variable.
Bitwise AND Assignment Example
let x = 10;
x &= 5;The |= Operator
The Bitwise OR Assignment Operator does a bitwise OR operation on two operands and assigns the result to the variable.
Bitwise OR Assignment Example
let x = 10;
x |= 5;The ^= Operator
The Bitwise XOR Assignment Operator does a bitwise XOR operation on two operands and assigns the result to the variable.
Bitwise XOR Assignment Example
let x = 10;
x ^= 5;Binary Numbers
Binary numbers with only one bit set are 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 |
Joke
There are only 10 types of people in the world: those who understand binary and those who don't.
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);
}