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Double-Base Number System (DBNS)

  • Book Excerpt from "Generative AI in C++"
  • by David Spuler, Ph.D.

Double-Base Number System (DBNS)

The DBNS is an advanced number system, where a number is represented by two or more bases, rather than a normal base number with only a single base. In non-DBNS, decimal is base 10, and binary is base 2. But in DBNS, you can have a “base 2 and 3” number, which is the sum of multiples of 2 and 3.

You can also have more than 2 bases, in which case it is called the Multiple-Base Number System (MBNS). Note that there is also an extension of the logarithmic number system (LNS) called Multi-dimensional LNS (MDLNS).

Research papers on the double-base number system:

  1. R. Muscedere, G.A. Jullien,V. Dimitrov, W.C. Miller, 2000, Non-linear signal processing using index calculus DBNS arithmetic, Proc. of the 2090 SPIE conf: on Advanced Algorithms and Architectures in Signal Processing, San Diego, August 2000, https://spie.org/Publications/Proceedings/Paper/10.1117/12.406502?SSO=1
  2. R. Muscedere, G.A. Jullien, V.S. Dimitrov and W.C. Miller, 2000, On efficient techniques for difficult operations in one and two-digit DBNS index calculus, Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154), Oct. 2000, https://ieeexplore.ieee.org/document/910637
  3. Vassil Dimitrov, Graham Jullien, Roberto Muscedere, 2012, Multiple-Base Number System: Theory and Applications (Circuits and Electrical Engineering Book 2), Part of: Circuits and Electrical Engineering (2 books), Jan 24, 2012 https://www.amazon.com/Multiple-Base-Number-System-Applications-Engineering-ebook/dp/B00847CSAG/
  4. Jiajia Chen & Chip-Hong Chang, 2017, Double-Base Number System and Its Application in FIR Filter Design, Embedded Systems Design with Special Arithmetic and Number Systems, pp. 277–310, https://link.springer.com/chapter/10.1007/978-3-319-49742-6_11
  5. V. S. Dimitrov, G. A. Jullien, and W. C. Liller, 1999, Theory and applications of the double-base number system, IEEE Trans. Comput., vol. 48, no. 10, pp. 1098–1106, Oct. 1999. https://ieeexplore.ieee.org/document/805158
  6. Jiajia Chen; Chip-Hong Chang; Feng Feng; Weiao Ding; Jiatao Ding, 2015, Novel Design Algorithm for Low Complexity Programmable FIR Filters Based on Extended Double Base Number System, IEEE Transactions on Circuits and Systems I: Regular Papers ( Volume 62, Issue 1, January 2015), https://ieeexplore.ieee.org/document/6914616
  7. V. S. Dimitrov, L. Imbert, and A. Zakaluzny, 2007, Multiplication by a constant is sublinear, in Proc. 18th IEEE Symp. Comput. Arith., Montpellier, France, Jun. 2007, pp. 261–268. https://ieeexplore.ieee.org/abstract/document/4272873

For more research papers on double-base number systems, see also https://www.aussieai.com/research/advanced-ai-mathematics#dbns.

 

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