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Theory and Applications of the Double-Base Number System
October 1999 (vol. 48 no. 10)
pp. 1098-1106

Abstract—In this paper, we analyze some of the main properties of a double base number system, using bases 2 and 3; in particular, we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus for logarithmic-like arithmetic with considerable hardware reductions in look-up table size. We discuss the application of this number system in the area of digital signal processing; we illustrate the discussion with examples of finite impulse response filtering.

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Index Terms:
Double-base number system, index calculus, digital signal processing, FIR filters.
Citation:
Vassil S. Dimitrov, Graham A. Jullien, William C. Miller, "Theory and Applications of the Double-Base Number System," IEEE Transactions on Computers, vol. 48, no. 10, pp. 1098-1106, Oct. 1999, doi:10.1109/12.805158
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