Serial Binary Addition with Polynominally Bounded Weights

This paper presents a new approach to the problem of serial binary addition with feed-forward neural networks. It is shown that the serial binary addition, an important component to a number of applications such signal processing, of two n-bit operands with carry can be done by a feed-forward linear threshold gate based network with polynomially bounded weights, i.e. in the order of O(n k), associated with small delay and size. In particular, it is shown that the overall delay for the serial addition is k log n + n k log n serial cycles, with the serial cycle comprising a neuron and a latch. The implementation cost of the proposal is in the order of O(log n), in terms of linear threshold gates, and in the order of O(log 2 n), in terms of latches. The fan-in is in the order of O(log n).