XOR of Two Variables in Python

The XOR or exclusive is a Boolean logic operation widely used in cryptography and generating parity bits for error checking and fault tolerance. The operation takes in two inputs and produces a single output. The operation is bitwise traditionally but could be performed logically as well. This article will teach you how to get the logical XOR of two variables in Python.

XOR of Two Numbers

As XOR is a bitwise operator, it will compare bits of both integers bit by bit after converting them into binary numbers. The truth table for XOR (binary) is shown below:

The formula for XOR operation is:

XOR(A, B) = ( A .\overline{B}) + (B.\overline{A})

Performing the XOR of two integers is trivial in Python, as the language offers an operator, especially for this purpose, namely a caret ^. But this operation can also be achieved by using the operator module in Python.

Note: A few things to remember while performing the xor operation:

• The XOR should only be between homogeneous elements, i.e., their datatype should be the same. 
• The bool of a string will result in True if the string is non-empty and False if the string is empty.

Now let us see the XOR operation on different datatypes in Python.

XOR on Integers

The integer numbers are first converted into the binary numbers and then each bit is compared with one another. The final answer is then again converted back into the original integer form. The following code demonstrates the usage of a caret for performing the XOR of two integer variables.

Example: Firstly two variables were initialized containing 10 and 27 integer values. Then the xor of the two variables is obtained using the caret operator. The result of the operation is displayed.

# First integer
a = 10
# Second integer
b = 27

# Performing the xor and storing the result in separate variable
xor = a ^ b

print(xor)

Output:

17

Time complexity: O(1)

Space complexity: O(1)

XOR on Boolean

The XOR of two boolean variables is quite simple. The output of the XOR operation is either 0 or 1 which represents True or Flase respectively in boolean format. Hence, to get the logical XOR of boolean datatype, either True or False is provided as the input values.

Example: Firstly two boolean variables were initialized with a value and then the XOR operation is performed on them using the caret operator.

# First boolean
a = True
# Second boolean
b = False

# Performing the xor operation
xor = a ^ b

print(xor)

Output:

True

Time complexity: O(1)

Space complexity: O(1)

XOR on String

Since strings are a sequence, the datatype needs to be normalized for the operation to be performed on them. Therefore, the strings would be converted to bool, and then the xor operation could be performed on them. But due to this, the result of the operation would be binary, i.e., it would result in either True or False (unlike xor of integers where resultant value is produced).

Example: Firstly two strings are defined. One of them is an empty string. Then the strings are converted to the boolean datatype, and the xor operation is performed on them. The result is displayed. 

# First string
a = "Hello World!"
# Second string
b = ""

# Performing the xor operation
xor = bool(a) ^ bool(b)

print(xor)

Output:

True

Time complexity: O(n) 

Space complexity: O(n), where n is length of string

XOR of Two Variables using Operator Module

Python has an operator module, which provides a set of predefined functions for arithmetic, logical, bitwise and comparison operators. It also provides the XOR function of the bitwise operator which can be used to get the XOR of two variables.

Example: Firstly import the operator module. Then two variables are initialized with a value and then the XOR operation is performed on them using the operator modules’s xor function.

# import module
import operator

# First integer
a = 10
# Second integer
b = 27

# Performing the xor using operator module
xor = operator.xor(a,b)

print(xor)

Output:

17

Time complexity: O(1)

Space complexity: O(1)

Swapping Two Integers using XOR without Temporary Variable

The XOR bitwise operation in Python can also be used to swap two integers without using the temporary variable. Let us see how this works.

a = a ^ b
b = a ^ b
a = a ^ b

Swapping requires three expressions with the XOR operation.

1. XOR the two integers ‘a’ and ‘b’ and store its result in the integer ‘a’ itself.
2. Now XOR the updated value of ‘a’ with ‘b’. This will result in the original value of ‘a’, which is now stored in ‘b’.
3. Lastly, XOR ‘a’ with the now updated value of ‘b’ in previous step. The result will be the original value of ‘b’. which is now stored in ‘a’.

Example: Firstly two integers are initialized. Then using the above three steps, the swapping of two integers is done using the XOR caret operator. Finally, print the swapped integers.

# First integer
a = 10
# Second integer
b = 27

print("Before Swapping:")
print("a =", a)
print("b =", b)

# swapping integers using XOR
a = a ^ b
b = a ^ b
a = a ^ b

print("After Swapping:")
print("a =", a)
print("b =", b)

Output:

Before Swapping:
a = 10
b = 27
After Swapping:
a = 27
b = 10