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!
Video Explainer
As you go over the article, you can watch my explainer video here:
Example
In this example, you apply the bitwise right-shift operator to integer 32 shifting it by one position:
x = 32 # Shift by one position to the right res = x >> 1 print(res) # 16 # Shift by two positions to the right res = x >> 2 print(res) # 8
The bit representation of decimal 32
is "00100000"
. If you shift it by one position to the right, you obtain binary "
(decimal 16). If you shift by two positions to the right, you obtain binary 00010000
""
(decimal 8). Here’s the tabular explanation:00001000
"
x | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
x >> 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
x >> 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
Each row represents the resulting shifted binary representation of the original integer 32.
Representing Negative Integers in Binaries
Python uses so-called complementary binaries to represent negative integers. The first bit of a complementary binary is the sign (0: positive, 1: negative). All remaining bits encode the number. You write a negative number -x
as the bit pattern for (x-1)
and flip all bits from 1 to 0 and from 0 to 1 (complement).
Here are two simple examples:
- To represent
x = -1
using 8 bits you first calculate(1-1) = 0
and then flip all bits to calculate"11111111"
. - To represent
x = -10
using 8 bits you first calculate(10-1) = 9
which is"00001001"
in binary format. Then, you complement all bits to determine the negative (complementary) binary"11110110"
.
Let’s use this knowledge in a couple of examples to showcase the working of the bitwise XOR operator on negative integers:
Python Bitwise Right Shift on Negative Integers
Here’s the result of the bitwise right-shift operator x >> n
when applied to example negative integer operands x
and n
:
x (int) | n (int) | x (binary) | x >> n (binary) | x >> n (int) |
---|---|---|---|---|
-1 | 1 | 11111111 | 11111111 | -1 |
-2 | 1 | 11111110 | 11111111 | -1 |
-4 | 1 | 11111100 | 11111110 | -2 |
-4 | 2 | 11111100 | 11111111 | -1 |
You can see those examples in the following script:
print(-1 >> 1) # -1 print(-2 >> 1) # -1 print(-4 >> 1) # -2 print(-4 >> 2) # -1
How to Resolve ValueError: negative shift count?
You cannot use a negative shift count, i.e., in the expression x >> n
, the second operand n must be non-negative. It can be zero. If you use a negative shift count, Python raises the “ValueError: negative shift count
“. To resolve it, use the left-shift operation x << n
instead of using a negative shift count.
Here’s an example of the ValueError
:
>>> 2 >> -1 Traceback (most recent call last): File "<pyshell#19>", line 1, in <module> 2 >> -1 ValueError: negative shift count
And here’s an example of how to resolve it using right-shift instead of left-shift operation:
>>> 2 << 1 4
Python Bitwise Right-Shift Operator Overloading
To enable the right-shift operator on your custom object, use Python’s operator overloading functionality. Overloading works through what is called magic methods or dunder methods (for “double-underscore methods”). For the right-shift operator, the magic method is the __rshift__(self, other)
method. It should return a new custom object that is the result of the bitwise operation.
Here’s a short overview of the Bitwise operators’ magic methods:
Bitwise Operator | Magic “Dunder” Method |
---|---|
& | __and__(self, other) |
| | __or__(self, other) |
^ | __xor__(self, other) |
~ | __invert__(self) |
<< | __lshift__(self, other) |
>> | __rshift__(self, other) |
Here’s an example of how to accomplish these bitwise operators on a custom class Data
. We marked this respective operator in the code:
class Data: def __init__(self, data): self.data = data def __and__(self, other): return Data(self.data & other.data) def __or__(self, other): return Data(self.data | other.data) def __xor__(self, other): return Data(self.data ^ other.data) def __invert__(self): return Data(~self.data) def __lshift__(self, other): return Data(self.data << other.data) def __rshift__(self, other): return Data(self.data >> other.data) x = 2 y = 3 print('Operands: \n', 'x =', x, '\n', 'y =', y) print() print('Bitwise AND: ', x & y) print('Bitwise OR: ', x | y) print('Bitwise XOR: ', x ^ y) print('Bitwise NOT: ', ~x) print('Bitwise LEFT-SHIFT: ', x << y) print('Bitwise RIGHT-SHIFT: ', x >> y)
The output is:
Operands: x = 2 y = 3 Bitwise AND: 2 Bitwise OR: 3 Bitwise XOR: 1 Bitwise NOT: -3 Bitwise LEFT-SHIFT: 16 Bitwise RIGHT-SHIFT: 0
Bitwise Operators
Bitwise operators perform operations on the binary (bit) representation of integers. The following table gives a short overview of all existing bitwise operators. Note that we also provide the binary representation 100
for the decimal integer 4
, and 101
for the decimal integer 5
as a comment in the right column.
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 |

While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.
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