What is the XOR bitwise operator?

What are bitwise operations?

We can perform Bitwise operations on one or two numbers on their binary level.

• The following operators need two operands:

  • AND (&)
  • OR (|)
  • XOR (^)
  • Left shift (<<)
  • Right shift (>>)

• The following operator needs one operand.

  • 1’s complement ( ~ )

XOR

XOR (^), or eXclusive OR, is a bitwise operator that returns true (1) for odd frequencies of 1.

The XOR truth table is as follows:

• 1 ^ 1 = 0
• 1 ^ 0 = 1
• 0 ^ 1 = 1
• 0 ^ 0 = 0

Some examples of XOR are as follows:

1. (5 ^ 3)

   • 5 in binary = (101)
   • 3 in binary = (011)
   • (101)^(011) = (110)
   • (110) in decimal = 6
   • Thus, 5^3 = 6.

2. (10 ^ 2)

   • 10 in binary = (1010)
   • 2 in binary = (010)
   • (1010)^(010) = (1000)
   • (1000) in decimal = 8
   • Thus, 10^2 = 8.

XOR properties

1. XOR is commutative.

   • This means, a^b = b^a.

2. XOR is associative.

   • This means, a^(b^c) = (a^b)^c = (a^c)^b.

3. XOR is self-inverse.

   • This means, any number XOR’ed with itself evaluates to 0.

   • a^a = 0.

4. 0 is the identity element for XOR.

   • This means, any number XOR’ed with 0 remains unchanged.
   • a^0 = a.