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Bitwise Operations

  1. Bitwise
  2. Bitwise operation on numbers
  3. What is Bitwise used for?

1. Bitwise

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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

2. Bitwise operation on numbers

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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

3. What is Bitwise used for?

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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
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