How to bitwise XOR of hex numbers in Python?

The bitwise XOR is a binary operation that compares two binary numbers bit by bit and returns "1" if the bits are different, and "0" if they are the same. The XOR (exclusive OR) operation follows these rules ?

Hexadecimal is a numbering system that uses a base-16 representation for numeric values. This system has 16 symbols: 0-9 and A-F, where A=10, B=11, C=12, D=13, E=14, F=15.

Using the XOR Operator (^)

To perform bitwise XOR on hex numbers in Python, use the XOR operator (^). The 0x prefix indicates hexadecimal representation ?

# Hexadecimal numbers
a = 0x12ef  # 4847 in decimal
b = 0xabcd  # 43981 in decimal

# Perform XOR operation
result = a ^ b
print(f"0x{a:x} ^ 0x{b:x} = 0x{result:x}")
print(f"Decimal: {a} ^ {b} = {result}")

0x12ef ^ 0xabcd = 0xb922
Decimal: 4847 ^ 43981 = 47398

Step-by-Step Binary XOR

Let's see how the XOR operation works at the binary level ?

a = 0x12ef
b = 0xabcd

print(f"a = 0x{a:x} = {bin(a)}")
print(f"b = 0x{b:x} = {bin(b)}")
print(f"XOR result = 0x{a^b:x} = {bin(a^b)}")

# Show bit-by-bit comparison
print("\nBit-by-bit XOR:")
print(f"  {a:016b}  (a)")
print(f"^ {b:016b}  (b)")
print(f"  {'-'*16}")
print(f"  {a^b:016b}  (result)")

a = 0x12ef = 0b1001011101111
b = 0xabcd = 0b10101011110011101
XOR result = 0xb922 = 0b10111001001000010

Bit-by-bit XOR:
  0001001011101111  (a)
^ 1010101111001101  (b)
  ----------------
  1011100100100010  (result)

XOR with Multiple Hex Numbers

You can chain multiple XOR operations together ?

hex_numbers = [0x12ef, 0xabcd, 0x5a5a, 0xffff]
result = 0

# XOR all numbers together
for num in hex_numbers:
    result ^= num
    print(f"After XOR with 0x{num:x}: 0x{result:x}")

print(f"\nFinal result: 0x{result:x} ({result} in decimal)")

After XOR with 0x12ef: 0x12ef
After XOR with 0xabcd: 0xb922
After XOR with 0x5a5a: 0xe378
After XOR with 0xffff: 0x1c87

Final result: 0x1c87 (7303 in decimal)

Converting Between Hex and Binary

Here's how to work with different number formats ?

# Different ways to represent hex numbers
hex_string = "A1B2"
hex_int = int(hex_string, 16)  # Convert hex string to integer
hex_literal = 0xC3D4

print(f"Hex string: {hex_string}")
print(f"As integer: {hex_int}")
print(f"Hex literal: 0x{hex_literal:x}")

# XOR operations
result1 = hex_int ^ hex_literal
print(f"\nXOR result: 0x{result1:x}")
print(f"As hex string: {hex(result1)}")
print(f"As binary: {bin(result1)}")

Hex string: A1B2
As integer: 41394
Hex literal: 0xc3d4

XOR result: 0x6266
As hex string: 0x6266
As binary: 0b110001001100110

Conclusion

Use the XOR operator (^) to perform bitwise XOR on hexadecimal numbers in Python. The operation works at the binary level, comparing each bit position and returning 1 for different bits and 0 for same bits. Python handles the conversion between hex and binary automatically.