Serial binary multiplication with feed-forward neural networks

In this paper we propose no learning based neural networks for serial binary multiplication. We show that for \subarray-wise" generation of the partial product matrix and a data transmission rate of bits per cycle the serial multiplication of two n-bit operands can be computed in n serial cycles with an O(nn) size neural network, and maximum fan-in and weight values both in the order of O(log). The minimum delay for this scheme is in the order of d p n e + log n and it corresponds to a data transmission rate of d p n e bits per cycle. For \column-wise" generation of the partial product matrix and a data transmission rate of 1 bit per cycle the serial multiplication can be achieved in 2n ? 1 + (k + 1)dlog k ne delay with a (k + 1) n?1 k?1 size neural network, a maximum weight of 2 k and a maximum fan-in of 3k + 1. If a data transmission rate of bits per serial cycle is assumed we prove a delay of d 2n?1 e + (+ 1)dlog ne for a (+ 1)(n ? 1) size neural network, a maximum weight of 2 and a maximum fan-in of 3 + 1.