Publication 1999 Issue No. 12 - December Abstract - Two Operand Binary Adders with Threshold Logic
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Two Operand Binary Adders with Threshold Logic
December 1999 (vol. 48 no. 12)
pp. 1324-1337
 ASCII Text x José Fernández Ramos, Alfonso Gago Bohórquez, "Two Operand Binary Adders with Threshold Logic," IEEE Transactions on Computers, vol. 48, no. 12, pp. 1324-1337, December, 1999.
 BibTex x @article{ 10.1109/12.817389,author = {José Fernández Ramos and Alfonso Gago Bohórquez},title = {Two Operand Binary Adders with Threshold Logic},journal ={IEEE Transactions on Computers},volume = {48},number = {12},issn = {0018-9340},year = {1999},pages = {1324-1337},doi = {http://doi.ieeecomputersociety.org/10.1109/12.817389},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Two Operand Binary Adders with Threshold LogicIS - 12SN - 0018-9340SP1324EP1337EPD - 1324-1337A1 - José Fernández Ramos, A1 - Alfonso Gago Bohórquez, PY - 1999KW - Threshold logicKW - computer arithmeticKW - binary addersKW - logic designKW - threshold gateKW - neural networks.VL - 48JA - IEEE Transactions on ComputersER -

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