Formal Formulations

Introduction

The elementary approach for
exchanging the contents of two memory registers,
A and B,
is to declare a third register, say,
C,
and then:

Copy the contents of A into C; Copy the contents of B into A; Copy the contents of C into B;

This is a fine solution,
provided that creating another register is cheap.
However, if registers are expensive and CPU cycles are cheap,
then an alternative approach is available.

When three consecutative "Exclusive-Or" operations
are performed on the contents of two memory registers,
the effect is to exchange the contents of the two memory registers.

Proof

Exclusive Or Demonstration

Enter a value for A, B, and then click Exchange.

Exchanging Values
[ Introduction ][ Theorem ]
[ First Assignment ][ Second Assignment ][ Third Assignment ]

Other Links
[ Non-Numerical Arithmetic ][ Boundary Mathematics ]
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