Abstract
In this chapter fundamentals of Continuous Valued Number System (CVNS) are presented. This number system has been developed for analog arithmetic, and has been applied in implementing a series of mixed-signal neural networks. The CVNS multi-digit representation of analog values allows flexibility in implementation of analog circuits and reduces the demand on the accuracy requirements of analog implementations. Continuous values can be presented by a set of analog-digits. Analog-digits have information overlap with each other, which can be used for detection or correction of errors caused by implementation or arithmetic issues. The level of information overlap between the digits is the designer choice and can be adjusted based on the design requirements. Higher overlap between the digits means errors can be corrected to a higher degree; however, area and power requirements of the system increase. In this chapter principles of digit generation, CVNS addition, and CVNS multiplication are presented.
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Acknowledgements
The authors would like to acknowledge the use of the following source material.
• Parts of Sect. 7.5: Copyright © IEEE. All rights reserved. Reprinted, with permission, from B. Zamanlooy, A. Novak, M. Mirhassani, “Complexity Study of the Continuous Valued umber System Adders,” IEEE International Symposium on Multiple Valued Logic, 116–121, 2012.
• Sections 7.6 and 7.7: Copyright © IEEE. All rights reserved. Reprinted, with permission, from “CVNS Synapse Multiplier for Robust Neurochips with On-Chip Learning,” IEEE Transaction on Very Large Scale Integration (VLSI) System, Vol. 23, No. 11, pp. 2540–2551, 2015.
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Zamanlooy, B., Mirhassani, M. (2017). Robust Analog Arithmetic Based on the Continuous Valued Number System. In: Molahosseini, A., de Sousa, L., Chang, CH. (eds) Embedded Systems Design with Special Arithmetic and Number Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-49742-6_7
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