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In this paper we investigate the reduction of the size for small depth feed-forward linear threshold networks performing binary addition and related functions. For n bit operands we propose a depth-3 O(n/sup 2//log n) asymptotic size network for the binary addition with O polynomially bounded weights. We propose also a depth-3 addition of optimal O(n) asymptotic sits network and a depth-2 comparison of O(/spl radic/n) asymptotic size network, both with O(2/sup /spl radic/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 on occasions in weight requirements.