Bitwise operators are used to perform operations at the bit level.

These operators work on binary values (0 and 1).

Before performing a bitwise operation, Python converts decimal numbers into binary form.

The operation is then performed bit by bit.

Operator	Meaning
&	Bitwise AND
|	Bitwise OR
^	Bitwise XOR
~	Bitwise Complement
<<	Left Shift
>>	Right Shift

Consider the following example:

Decimal	Binary
4	100
5	101

The & operator returns 1 only when both bits are 1.

Otherwise, it returns 0.

Bit 1	Bit 2	Result
0	0	0
0	1	0
1	0	0
1	1	1

4 = 100
5 = 101

100
101
---
100

Binary 100 = Decimal 4
        

The | operator returns 1 if at least one bit is 1.

Bit 1	Bit 2	Result
0	0	0
0	1	1
1	0	1
1	1	1

4 = 100
5 = 101

100
101
---
101

Binary 101 = Decimal 5
        

The ^ operator returns 1 only when both bits are different.

Bit 1	Bit 2	Result
0	0	0
0	1	1
1	0	1
1	1	0

4 = 100
5 = 101

100
101
---
001

Binary 001 = Decimal 1
        

The ~ operator is also called the Bitwise NOT operator.

Formula:

~x = -(x + 1)

~4

= -(4 + 1)

= -5
        

The left shift operator shifts bits toward the left.

Formula:

x << n = x * 2ⁿ

10 * 2²

10 * 4

= 40
        

10 = 1010

After shifting 2 positions:

101000

Decimal = 40
        

The right shift operator shifts bits toward the right.

Formula:

x >> n = x // 2ⁿ

10 // 2²

10 // 4

= 2
        

10 = 1010

After shifting 2 positions:

10

Decimal = 2
        

• Bitwise operators work on binary values.
• They are mostly used in low-level programming.
• Shift operators are faster than multiplication and division in many low-level operations.
• The complement operator always returns a negative value.

Bitwise operators are commonly used in:

• Networking
• Cryptography
• Embedded systems
• Operating systems
• Image processing

Operator	Usage
&	Masking
|	Setting bits
^	Toggling bits
<<	Fast multiplication
>>	Fast division

Logical Operators	Bitwise Operators
Work on Boolean values.	Work on binary bits.
Examples: and, or	Examples: &, |

Operator	Purpose
&	Bitwise AND
|	Bitwise OR
^	Bitwise XOR
~	Bitwise Complement
<<	Left Shift
>>	Right Shift