Question

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How does XOR variable swapping work?

I found a solution to switching the values of two variables, without creating a third variable, which is as follows:

x ^= y;
y ^= x;
x ^= y;

This is using the exculsive-or operator (“XOR”), in a way other than boolean (I’m assuming it’s bitwise?). Having learned some Discrete Mathematics recently, I can understand the usage of the XOR operator with a truth-table:

.......................
    x  y  (x XOR y)
.......................
    T  T      F
    T  F      T
    F  T      T
    F  F      F

The expression (x XOR y) evaluates to false when both variables are equivalent, and to true otherwise. But WTF when the values are not boolean?

---

Anyway, if I set x and y equal to int values instead of boolean values, the operations are not very straightforward. So, for example let x = 3, and y = 5:

public class SwitchValues
{
    // instance methods
    public void SwitchBoolean(boolean x, boolean y)
    {
        System.out.println("The variable \"x\" is initially: " + x + ".\n" +
            "The variable \"y\" is initially: " + y + ".");
        x ^= y;
        System.out.println("x ^= y is equal to: " + x + ".");
        y ^= x;
        System.out.println("y ^= x is equal to: " + y + ".");
        x ^= y;
        System.out.println("x ^= y is now equal to: " + x + ".");

        System.out.println("The variable \"x\" is now: " + x + ".\n" +
            "The variable \"y\" is now: " + y + ".\n");
    } // end of SwitchBoolean

    public void SwitchInts(int x, int y)
    {
        System.out.println("The variable \"x\" is initially: " + x + ".\n" +
            "The variable \"y\" is initially: " + y + ".");
        x ^= y;
        System.out.println("x ^= y is equal to: " + x + ".");
        y ^= x;
        System.out.println("y ^= x is equal to: " + y + ".");
        x ^= y;
        System.out.println("x ^= y is now equal to: " + x + ".");

        System.out.println("The variable \"x\" is now: " + x + ".\n" +
            "The variable \"y\" is now: " + y + ".\n");
    } // end of SwitchInts

    // main method
    public static void main(String[] args)
    {
        SwitchValues obj = new SwitchValues();

        obj.SwitchBoolean(true, false);
        obj.SwitchInts(3, 5);

    } // end of main method
} // end of class SwitchValues

… and the results printed out for the int values are as follows:

The variable "x" is initially: 3.
The variable "y" is initially: 5.
x ^= y is equal to: 6.
y ^= x is equal to: 3.
x ^= y is now equal to: 5.
The variable "x" is now: 5.
The variable "y" is now: 3.

Answer 1

Actually you gave the answer yourself. You assumed xor on int is bitwise and thats correct. Transform the numbers to bit representation and then apply the xor bit by bit.

3 is 11 in binary. 5 is 101 in binary

011
101
--- xor
110

110 is 6 in decimal.

If you want to know how to calculate the binary represantation of a number you should look up Horner’s method. Its quite easy to do.