Python Program to Find XOR of Two Numbers

You can find the XOR of two numbers in Python using the ^ operator like this: result = a ^ b.

Examples

Inputa = 5, b = 3

Output6

Inputa = 10, b = 10

Output0

Inputa = 0, b = 7

Output7

How to Think About It

To find the XOR of two numbers, think of comparing their bits. The XOR operator ^ returns 1 for each bit position where the bits of the two numbers differ, and 0 where they are the same. So, the result is a new number representing these differences.

Algorithm

1

Get the first number as input.

2

Get the second number as input.

3

Apply the XOR operator <code>^</code> between the two numbers.

4

Store the result.

5

Return or print the result.

Code

python

a = int(input("Enter first number: "))
b = int(input("Enter second number: "))
result = a ^ b
print("XOR of", a, "and", b, "is", result)

Output

Enter first number: 5
Enter second number: 3
XOR of 5 and 3 is 6

Dry Run

Let's trace the example where a = 5 and b = 3 through the code.

1

Input numbers

a = 5, b = 3

2

Apply XOR operator

5 in binary is 0101, 3 in binary is 0011; XOR is 0110 which is 6

3

Print result

Output: XOR of 5 and 3 is 6

a (decimal)	b (decimal)	a (binary)	b (binary)	a ^ b (binary)	a ^ b (decimal)
5	3	0101	0011	0110	6

Why This Works

Step 1: XOR operator basics

The ^ operator compares bits of two numbers and returns 1 if bits differ, else 0.

Step 2: Bitwise comparison

Each bit of the two numbers is compared independently to produce the result.

Step 3: Result formation

The resulting bits form a new number representing the XOR of the inputs.

Alternative Approaches

Using a function

python

def xor_two_numbers(x, y):
    return x ^ y

print(xor_two_numbers(5, 3))

This approach makes the code reusable and clearer for multiple XOR operations.

Using bitwise operations manually

python

def manual_xor(x, y):
    result = 0
    power = 1
    while x > 0 or y > 0:
        bit_x = x % 2
        bit_y = y % 2
        xor_bit = (bit_x + bit_y) % 2
        result += xor_bit * power
        x //= 2
        y //= 2
        power *= 2
    return result

print(manual_xor(5, 3))

This shows how XOR works bit by bit but is less efficient and more complex.

Complexity: O(1) time, O(1) space

Time Complexity

XOR operation is a single CPU instruction working on fixed-size integers, so it runs in constant time.

Space Complexity

No extra memory is needed besides a variable to store the result, so space is constant.

Which Approach is Fastest?

Using the built-in ^ operator is fastest and simplest compared to manual bitwise methods.

Approach	Time	Space	Best For
Using ^ operator	O(1)	O(1)	Simple and fast XOR
Function wrapper	O(1)	O(1)	Reusable code
Manual bitwise method	O(log n)	O(1)	Educational, bit-level understanding