2-1 Additions and Related Arithmetic Operations with Threshold Logic

In this paper we investigate the reduction of the size for small depth feed-forward linear threshold networks performing binary addition, comparison, and related functions. For n bit operands we propose a depth-3 O(n 2 log n) asymptotic size network for the binary addition with polynomially bounded weights. We propose also a depth-3 addition of optimal O(n) asymptotic size network and a depth-2 comparison of O(p n) asymptotic size network, both with O(2 p n) asymptotic size of weight values. For existing architectural formats we show that our schemes, with equal or smaller depth networks, substantially outperform existing schemes in terms of size and fan-in requirements and in occasions in weight requirements.