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Aryan Saèd, Majid Ahmadi, Graham A. Jullien, "A Number System with Continuous Valued Digits and Modulo Arithmetic," IEEE Transactions on Computers, vol. 51, no. 11, pp. 12941305, November, 2002.  
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@article{ 10.1109/TC.2002.1047754, author = {Aryan Saèd and Majid Ahmadi and Graham A. Jullien}, title = {A Number System with Continuous Valued Digits and Modulo Arithmetic}, journal ={IEEE Transactions on Computers}, volume = {51}, number = {11}, issn = {00189340}, year = {2002}, pages = {12941305}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2002.1047754}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  A Number System with Continuous Valued Digits and Modulo Arithmetic IS  11 SN  00189340 SP1294 EP1305 EPD  12941305 A1  Aryan Saèd, A1  Majid Ahmadi, A1  Graham A. Jullien, PY  2002 KW  Computer arithmetic KW  continuous digits KW  modulo arithmetic KW  multiplevalued logic KW  lownoise circuitry. VL  51 JA  IEEE Transactions on Computers ER   
Abstract—This paper presents a novel number system based on signed continuous valued digits. Arithmetic operations in this number system are performed using simple analog circuitry, in contrast to the conventional implementation of arithmetic units by Boolean or multiplevalued logic circuits. Unlike the limited precision offered by classical analog arithmetic circuits, the ensemble of continuous valued digits that comprises a number in this system provides arbitrary implementation precision with standard analog circuitry. The number system also provides almostcarryfree arithmetic structures with digit level redundancy. In this paper, we introduce the mathematical foundations for positive and negative numbers, addition, multiplication, redundancy, radix conversions, and also the digit value integrity for circuit implementations. Potential applications are in the area of low noise and low crosstalk circuitry for arithmetic circuits used in mixedsignal systems.
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