<p><b>Abstract</b>—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 <it>n</it> bit operands we propose a depth-3 <tmath>$O({\textstyle{{n^2} \over {\log\,n}}})$</tmath> asymptotic size network for the binary addition with polynomially bounded weights. We propose also a depth-3 addition of optimal <it>O</it>(<it>n</it>) asymptotic size network and a depth-2 comparison of <tmath>$O({\sqrt n})$</tmath> asymptotic size network, both with <tmath>$O(2^{\sqrt n})$</tmath> 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.</p>