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Two Operand Binary Adders with Threshold Logic
December 1999 (vol. 48 no. 12)
pp. 1324-1337

Abstract—The central topic of this paper is the implementation of binary adders with Threshold Logic using a new methodology that introduces two innovations: the use of the input and output carries of each bit for obtaining all the sum bits and a modification of the classic Carry Lookahead adder technique that allows us to obtain the expressions of the generation and propagation carries in a more appropriate way for Threshold Logic. In this way, it has been possible to systematize the process of design of a binary adder with Threshold Logic relating all its important parameters: number of bits of the operands, depth, size, maximum fan-in, and maximum weight. The results obtained are an improvement on those published to date and are summarized as follows: Depth 2 adder: $s = 2n$, $w_{max} = 2^n$, $f_{max} = 2n + 1$. Depth 3 adder: $s = 4n - 2\left\lceil {{n \over {\left\lceil {\sqrt n } \right\rceil }}} \right\rceil $, $w_{\max } = 2^{\left\lceil {{n} \over {\left\lceil {\sqrt n } \right\rceil }}} \right\rceil } $, $f_{\max } = 2\left\lceil {{n \over {\left\lceil {\sqrt n } \right\rceil }}} \right\rceil + 1$. Depth d adder (asymptotic behavior): $s = O (n)$, $w_{\max } = O(2^{\root {d - 1} \of n } )$, $f_{\max } = O(\root {d - 1} \of n )$. If the weights are bounded by $w_{max}$: $n_{\max } = O\!\left( {\log ^{d - 1} w_{\max } } \right)$, $d_{\min } = O\!\left( {{{\log n} \over {\log \left( {\log w_{\max } } \right)}}} \right)$.

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Index Terms:
Threshold logic, computer arithmetic, binary adders, logic design, threshold gate, neural networks.
José Fernández Ramos, Alfonso Gago Bohórquez, "Two Operand Binary Adders with Threshold Logic," IEEE Transactions on Computers, vol. 48, no. 12, pp. 1324-1337, Dec. 1999, doi:10.1109/12.817389
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