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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.
Citation:
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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