The Python bitwise right-shift operator
x >> n shifts the binary representation of integer
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
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!
As you go over the article, you can watch my explainer video here:
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
"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
" (decimal 8). Here’s the tabular explanation:
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 = -1using 8 bits you first calculate
(1-1) = 0and then flip all bits to calculate
- To represent
x = -10using 8 bits you first calculate
(10-1) = 9which is
"00001001"in binary format. Then, you complement all bits to determine the negative (complementary) binary
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
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
>>> 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|
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 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
101 for the decimal integer
5 as a comment in the right column.
|&||Bitwise AND||Performs logical AND on a bit-by-bit basis|
||||Bitwise OR||Performs logical OR operation on a bit-by-bit basis|
|~||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 |
|^||Bitwise XOR||Performs logical “exclusive or” operation on a bit-by-bit basis|
|>>||Bitwise right shift||Shifts binary of left operand to the right by the number of positions specified in right operand|
|<<||Bitwise left shift||Shifts binary of left operand to the left by the number of positions specified in right operand|
While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.
To help students reach higher levels of Python success, he founded the programming education website Finxter.com. He’s author of the popular programming book Python One-Liners (NoStarch 2020), coauthor of the Coffee Break Python series of self-published books, computer science enthusiast, freelancer, and owner of one of the top 10 largest Python blogs worldwide.
His passions are writing, reading, and coding. But his greatest passion is to serve aspiring coders through Finxter and help them to boost their skills. You can join his free email academy here.