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
As you go over the article, you can watch my explainer video here:
In this example, you apply the bitwise NOT operator to integer 32:
>>> ~32 -33
~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.
How do you transform the binary “1011111” to a decimal number again? By using the following steps:
- Flip each bit back to
- Get the corresponding decimal number
- Increase it by one to
- Prefix it with the negative symbol
To understand this inverse method from a negative binary to an integer, you need to learn some background first. But don’t worry, it’s just a couple of minutes! ?
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
? In fact, Python uses signed integers for its bitwise operators. You may ask: what are signed integers?
- A signed integer, for example using 32 bits, encodes an integer in the range
[-2147483648 to 2147483647].
- An unsigned integer encodes a positive integer in the range
[0 to 4294967295]. The signed integer is represented in twos complement notation.
Python Bitwise NOT Operator Example
Here’s the result of the bitwise NOT operator
~x when applied to a couple of example integer operands
|x (int)||x (binary)||~x (binary)||~x (int)|
You can see those examples in the following Python script:
>>> ~0 -1 >>> ~1 -2 >>> ~3 -4 >>> ~9 -10 >>> ~11 -12 >>> ~256 -257
Let’s use this knowledge in a couple of examples to showcase the working of the bitwise NOT operator on negative integers:
Python Bitwise NOT Examples on Negative Integers
Here’s the result of the bitwise NOT operator
~x when applied to a negative integer operand
|x (int)||~x (int)|
You can see those examples in the following script:
>>> ~-0 -1 >>> ~-1 0 >>> ~-3 2 >>> ~-9 8 >>> ~-11 10 >>> ~-256 255
Python Bitwise NOT Overloading
You can define your own bitwise NOT operator on a custom class by overloading the
__invert__ method (dunder method, magic method) with a reference to
self as an argument. This allows the expression
~x on your custom objects without raising an error.
Here’s an example:
class Data: def __init__(self, data): self.data = data def __invert__(self): return Data(~self.data) x = Data(3) res = ~x print(res.data) # -4
Note: if you forget to overwrite the
__invert__ method and still try to use the expression
~x, Python will raise a
TypeError: bad operand type for unary ~. You can fix it by defining the dunder method
__invert__(self) in your class definition.
class Data: def __init__(self, data): self.data = data x = Data(3) res = ~x print(res.data)
Traceback (most recent call last): File "C:\Users\xcent\Desktop\code.py", line 8, in res = ~x TypeError: bad operand type for unary ~: 'Data'
To fix this
TypeError, simply define the
__invert__ method as shown in the previous working example.
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|
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
While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.
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