As an application of the property that a " a = 0 for any bit vector a, consider the following program:

As the name implies, we claim that the effect of this procedure is to swap the values stored at the locations denoted by pointer variables x and y. Note that unlike the usual technique for swapping two values, we do not need a third location to temporarily store one value while we are moving the other. There is no performance advantage to this way of swapping; it is merely an intellectual amusement. Starting with values a and b in the locations pointed to by x and y, respectively, fill in the table that follows, giving the values stored at the two locations after each step of the procedure. Use the properties of ᵔ to show that the desired effect is achieved. Recall that every element is its own additive inverse (that is, a ᵔ a = 0).

1 2 3 4 5 void inplace_swap (int *x, int *y) { *y = *x /* Step 1 */ /* Step 2 */ /* Step 3 */ } *y = *x ~ *y; *y; *y;