A possible nanometer-scale computing device based on an adding cellular automaton

We present a simple one-dimensional cellular automaton (CA) which has the property that an initial state composed of two binary numbers evolves quickly into a final state which is their sum. We call this CA the adding cellular automaton (ACA). The ACA requires only 2N two-state cells in order to add any two N−1 bit binary numbers. The ACA could be directly realized as a wireless nanometer-scale computing device. A possible implementation using coupled quantum dots is outlined.