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2-1 Addition and Related Arithmetic Operations with Threshold Logic
September 1996 (vol. 45 no. 9)
pp. 1062-1067

Abstract—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 $O({\textstyle{{n^2} \over {\log\,n}}})$ 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 $O({\sqrt n})$ asymptotic size network, both with $O(2^{\sqrt n})$ 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.

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Index Terms:
Computer arithmetic, binary adders, binary comparison, majority circuits, threshold logic, neural networks.
Stamatis Vassiliadis, Sorin Cotofana, Koen Bertels, "2-1 Addition and Related Arithmetic Operations with Threshold Logic," IEEE Transactions on Computers, vol. 45, no. 9, pp. 1062-1067, Sept. 1996, doi:10.1109/12.537130
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