Bitwise operators perform operations on the binary (bit) representation of integers.

**Background**: Each integer is first written as a binary number that is a sequence of digits 0 or 1. For example:

- 0 is written as “0”
- 1 is written as “1”
- 2 is written as “10”
- 3 is written as “11”
- 4 is written as “100”
- 5 is written as “101”

The bitwise operators are then applied on those binary representations. The resulting binary number is then converted back to the integer representation (decimal number).

In the following table, we exemplify all bit-wise operators with variables `x`

and `y`

defined as follows:

>>> x = 4 # 100 >>> y = 5 # 101

As a comment, we also provide the binary representation `100`

for the decimal integer `4`

, and `101`

for the decimal integer `5`

.

Operator | Name | Description | Example |
---|---|---|---|

`x = 4, y = 5` | |||

& | Bitwise AND | Performs logical AND on a bit-by-bit basis | `x & y` |

| | Bitwise OR | Performs logical OR operation on a bit-by-bit basis | `x | y` |

~ | Bitwise NOT | Performs logical NOT on a bit-by-bit basis, inverting each bit so that 0 becomes 1 and 1 becomes 0. Same as `-x-1` . | `~x` |

^ | Bitwise XOR | Performs logical “exclusive or” operation on a bit-by-bit basis | `x ^ y` |

>> | Bitwise right shift | Shifts binary of left operand to the right by the number of positions specified in right operand | `x >> 2` |

<< | Bitwise left shift | Shifts binary of left operand to the left by the number of positions specified in right operand | `x << 2` |

Let’s dive into these bitwise operators one by one:

Table of Contents

## Bitwise AND

Python’s ** bitwise AND** operator

`x & y`

performs *logical AND*on each bit position on the binary representations of integers

`x`

and `y`

. Thus, each output bit is 1 if both input bits at the same position are 1, otherwise, it’s 0. For example, the integer expression 4 & 3 is translated to binaries 0100 & 0011 which results in 0000 because all four input bit positions are different. In this example, you apply the ** bitwise AND **operator to two integers 32 and 16:

>>> 32 & 16 0

The expression `32 & 16`

operates on the bit representations `"010000"`

(decimal 32) and `"001000"`

(decimal 16) and performs ** bitwise AND**. As all i-th bit positions are different, the result is 0:

First Operand `x` | 1 | 0 | 0 | 0 | 0 | 0 |

Second Operand `y` | 0 | 1 | 0 | 0 | 0 | 0 |

`x & y` | 0 | 0 | 0 | 0 | 0 | 0 |

For more examples and a more detailed explanation of the operator, check out our detailed blog guide.

**Full Guide:** Python Bitwise AND Operator

## Bitwise OR

Python’s ** bitwise OR** operator

`x | y`

performs *logical OR*on each bit position on the binary representations of integers

`x`

and `y`

. Each output bit evaluates to 1 *if and only if*at least one of the two input bits at the same position are 1. For example, the integer expression

`4 | 3`

is translated to the binary operation `0100 | 0011`

which results in `0111`

because for the last three positions at least one bit is 1. In this example, you apply the ** bitwise OR **operator to two integers 32 and 16:

>>> 32 | 16 48

The expression `32 | 16`

operates on the bit representations `"010000"`

(decimal 32) and `"001000"`

(decimal 16) and performs ** bitwise OR**. Each

`"1"`

position propagates remains in the result `"110000"`

(decimal 48):First Operand `x` | 1 | 0 | 0 | 0 | 0 | 0 |

Second Operand `y` | 0 | 1 | 0 | 0 | 0 | 0 |

`x | y` | 1 | 1 | 0 | 0 | 0 | 0 |

For more examples and a more detailed explanation of the operator, check out our detailed blog guide.

**Full Guide:** Python Bitwise OR Operator

## Bitwise NOT

Python’s ** bitwise NOT** operator

`~x`

inverts each bit from the binary representation of integer `x`

so that 0 becomes 1 and 1 becomes 0. This is semantically the same as calculating `~x == -x-1`

. For example, the bitwise NOT expression `~0`

becomes `-1`

, `~9`

becomes `-10`

, and `~32`

becomes `-33`

. In this example, you apply the ** bitwise NOT **operator to integer 32:

>>> ~32 -33

The expression `~32`

operates on the bit representations `"0100000"`

(decimal 32) and performs ** bitwise NOT** resulting in binary

`"1011111"`

. This corresponds to the negative decimal number -33. `x` | 0 | 1 | 0 | 0 | 0 | 0 | 0 |

`~x` | 1 | 0 | 1 | 1 | 1 | 1 | 1 |

How do you transform the binary “1011111” to a decimal number again? By using the following steps:

- Flip each bit back to
`0100000`

. - Get the corresponding decimal number
`32`

. - Increase it by one to
`33`

. - Prefix it with the negative symbol
`-33`

.

For more examples and a more detailed explanation of the operator, check out our detailed blog guide.

**Full Guide:** Python Bitwise NOT Operator

## Bitwise XOR

Python’s ** bitwise XOR** operator

`x ^ y`

performs *logical XOR*on each bit position on the binary representations of integers

`x`

and `y`

. Each output bit evaluates to 1 *if and only if*exactly one of the two input bits at the same position are 1. For example, the integer expression

`4 ^ 3`

is translated to the binary operation `0100 ^ 0011`

which results in `0111`

because for the last three positions exactly one bit is 1. In this example, you apply the ** bitwise XOR **operator to two integers 32 and 16:

>>> 32 ^ 16 48

The expression `32 ^ 16`

operates on the bit representations `"0100000"`

(decimal 32) and `"0010000"`

(decimal 16) and performs ** bitwise XOR** resulting in binary

`"0110000"`

(decimal 48):First Operand `x` | 1 | 0 | 0 | 0 | 0 | 0 |

Second Operand `y` | 0 | 1 | 0 | 0 | 0 | 0 |

`x ^ y` | 1 | 1 | 0 | 0 | 0 | 0 |

**Full Guide:** Python Bitwise XOR Operator

## Bitwise Right-Shift

The Python ** bitwise right-shift** operator

`x >> n`

shifts the binary representation of integer `x`

by `n`

positions to the right. It inserts a `0`

bit on the left and removes the right-most bit. For example, if you right-shift the binary representation `0101`

by one position, you’d obtain `0010`

. Semantically, the bitwise right-shift operator is the same as performing integer division by `2**n`

. Here’s a minimal example:

print(8 >> 1) # 4 print(8 >> 2) # 2 print(-3 >> 1) # -2

Let’s dive deeper into the details next!

**Full Guide:** Python Bitwise Right-Shift Operator

## Bitwise Left-Shift

The Python ** bitwise left-shift** operator

`x << n`

shifts the binary representation of integer `x`

by `n`

positions to the left. For a positive integer, it inserts a `0`

bit on the right and shifts all remaining bits by one position to the left. For example, if you left-shift the binary representation `0101`

by one position, you’d obtain `01010`

. Semantically, the bitwise left-shift operator `x << n`

is the same as multiplying the integer `x`

with `2**n`

. Here’s a minimal example:

print(8 << 1) # 16 print(8 << 2) # 32 print(-3 << 1) # -6

As you go over the article, you can watch my explainer video here:

**Full Guide:** Python Bitwise Left-Shift Operator

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