XOR

Abstract

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• Exclusive OR, difference

$$B-A=\{x\in U:x\in B\wedge x\notin A\}$$

• Returns true only when 2 inputs aren’t the same

Properties

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Self-Inverse

• a ^ a = 0
• a XOR a is always 0

Own-Inverse

• a ^ b ^ b = a
• W always get back the another half by XOR the another half one more time. Because Self-Inverse, b ^ b = 0

Tricks

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Swapping values

public class MyClass {
    public static void main(String args[]) {
      int x=10;
      int y=25;
      
      x = x ^ y; // x ^ x = y, x ^ y = x
      y = x ^ y; // x
      x = x ^ y; // y
 
      System.out.println("x: " + x);
      System.out.println("y: " + y);
    }
}