Table Of Content
Bitwise Operations
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In digital computer programming. The bitwise operation works on one or more binary numerals, or binary numerals-like strings. This is a simple and fast operation, directly supported by processor. Normally, bitwise operations are much faster than multiplication, division, sometimes significantly faster than addition. bitwise calculations use less energy because it rarely uses resources.
There are 7 bitwise operations :
| Operator | Name | Description |
|---|---|---|
| & | AND | If both bits are 1, the return value is 1, otherwise it returns 0. |
| | | OR | If one of two bits is 1, the return value is 1, otherwise it returns 0. |
| ^ | XOR | If 2 bits are different, the return value is 1, otherwise it returns 0. |
| ~ | NOT | Inverts all the bits, 0 to 1 and 1 to 0. |
| << | Zero fill left shift | Shifts all bits to the left. |
| >> | Signed right shift | Shifts all bits to the right except the first bit. |
| >>> | Zero fill right shift | Shifts all bits to the right. |
Bitwise AND
When a bitwise AND is performed on a pair of bits, it returns 1 if both bits are 1, otherwise returns 0.
Example with 1 bit:
| Operation | Result |
|---|---|
| 0 & 0 | 0 |
| 0 & 1 | 0 |
| 1 & 0 | 0 |
| 1 & 1 | 1 |
Example with 4 bit:
| 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, otherwise returns 0.
Example with 1 bit:
| Operation | Result |
|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Example with 4 bits:
| 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, otherwise returns 0.
Example with 1 bit:
| Operation | Result |
|---|---|
| 0 ^ 0 | 0 |
| 0 ^ 1 | 1 |
| 1 ^ 0 | 1 |
| 1 ^ 1 | 0 |
Example with 4 bits:
| Operation | Result |
|---|---|
| 1111 ^ 0000 | 1111 |
| 1111 ^ 0001 | 1110 |
| 1111 ^ 0010 | 1101 |
| 1111 ^ 0100 | 1011 |
Bitwise NOT
When a Bitwise NOT is used, it will reverse all bits, 1 to 0, and 0 to 1.
Example with 1 bit:
| Operation | Result |
|---|---|
| ~ 0 | 1 |
| ~ 1 | 0 |
Example with 4 bits:
| Operation | Result |
|---|---|
| ~ 0000 | 1111 |
| ~ 0001 | 0001 |
| ~ 0010 | 1101 |
| ~ 1100 | 0011 |
Different languages can have multiple data types to represent numbers.
- Java: byte, short, int, long, double.
- C#: byte, sbyte, short, ushort, int, uint, long, ulong, float, double
- Javascript: double
- .....
Javascript stores numbers as 64 bits floating point numbers. But bitwise operations are performed on 32-bit integers. Other languages such as Java, C#,.. bitwise operations are also performed on 32-bit integers.
Therefore, before carrying out the bitwise operations with numbers, you have to convert each number into a sequence of 32 binary numbers.
| Base 10 | Base 2 | 32 bits |
| 5 | 101 | 00000000000000000000000000000101 |
| 218 | 11011010 | 00000000000000000000000011011010 |
In Javascript, the toString(base) method helps you change any number from base 10 to other base.
toString-base-example.js (Javascript)
let a = 8;
// Base 2 string.
console.log( a.toString(2) );// 1000
// Base 8 string
console.log( a.toString(8) ); // 10
// Base 16 string
console.log( a.toString(16) ); // 8
let b = 218;
// Base 2 string.
console.log( b.toString(2) );// 11011010
// Base 8 string
console.log( b.toString(8) ); // 332
// Base 16 string
console.log( b.toString(16) ); // da
Example:
| Decimal | Binary |
|---|---|
| 5 | 00000000000000000000000000000101 |
| 1 | 00000000000000000000000000000001 |
| 5 & 1 = 1 | 00000000000000000000000000000001 |
| 5 | 1 = 5 | 00000000000000000000000000000101 |
| 5 ^ 1 = 4 | 00000000000000000000000000000100 |
| ~ 5 = -6 | 11111111111111111111111111111010 |
Note: Of 32 bits, the first bit is used to determine the sign of number. If this bit is 1, it corresponds to the ( - ) sign. If this bit is 0 , it corresponds to the ( + ) sign
Bitwise Left Shift (<<)
| Decimal | Binary |
|---|---|
| 5 | 00000000000000000000000000000101 |
| 5 << 1 = 10 | 00000000000000000000000000001010 |
| 5 << 2 = 20 | 00000000000000000000000000010100 |
The Bitwise Left Shift ( << ) Operator can change the sign of number.
(Javascript code)
console.log( 1073741824 << 1); // -2147483648
console.log( 2684354560 << 1); // 1073741824
Bitwise Right Shift (>>) [Unsigned Right Shift]
| Decimal | Binary |
|---|---|
| 29 | 00000000000000000000000000011101 |
| 29 >> 1 = 14 | 00000000000000000000000000001110 |
| 29 >> 2 = 7 | 00000000000000000000000000000111 |
The Bitwise Right Shift ( >> ) operator doesn't change the sign of number because the first bit is not moved.
Bitwise Right Shift (>>>) [Zero fill right Shift]
The Bitwise Right Shift ( >>> ) operator can change the number sign.
(Javascript Code)
console.log( -1073741824 >>> 1); // 1610612736
console.log( 1073741824 >>> 1); // 536870912
The bitwise calculations are directly supported by the computer processor, it performs very fast. Below, I list some examples of using these calculations.
Use the bitwise operations on Strings (characters) in the Java, C#, C/C++ ...languages. Note: some languages such as Javascript don't support the bitwise operation with String type.
Convert an Uppercase into Lowercase:
// Rule: x | ' '
('A' | ' ') ==> 'a'
('B' | ' ') ==> 'b'
('a' | ' ') => 'a'
Convert Lowercase into Uppercase:
// Rule: x & '_'
('a' & '_') ==> 'A'
('b' & '_') ==> 'B'
('A' & '_') ==> 'A'
Reverse uppercase to lowercase, lowercase to uppercase:
// Rule: x ^ ' '
('a' ^ ' ') ==> 'A'
('A' ^ ' ') ==> 'a'
View the position of Latin letters (applying to only uppercase)
// Rule: x & '?'
'A' & '?' ==> 1
'B' & '?' ==> 2
...
'Z' & '?' ==> 26
// Rule: x ^ '@'
'A' ^ '@' ==> 1
'B' ^ '@' ==> 2
...
'Z' ^ '@' ==> 26
View the position of Latin letters (applying only to lowercase)
// Rule: x ^ '`'
'a' ^ '`' ==> 1
'b' ^ '`' ==> 2
...
'z' ^ '`' ==> 26
// '`' : binary ( 1100000 ), hex('60'), chr(96)
View the position of Latin letters, applying to both uppercase and lowercase:
// Rule: x & '\u001F'
'A' & '\u001F' ==> 1
'B' & '\u001F' ==> 2
...
'Z' & '\u001F' ==> 26
'A' & '\u001F' ==> 1
'B' & '\u001F' ==> 2
...
'Z' & '\u001F' ==> 26
