On Serial Multiplication with Neural Networks

In this paper we propose no learning based neural networks for serial multiplication. We show that for “subarray-wise” generation of the partial product matrix and a data transmission rate of -bit per cycle the serial multiplication of two n-bit operands can be computed in n serial cycles with an O(n ) 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 dpn e+ log n and it corresponds to a data transmission rate of dpn e-bit 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)dlogk ne delay with a (k+1)n 1 k 1 size neural network, a maximum weight of 2k and a maximum fan-in of 3k+1. If a data transmission rate of -bit 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.