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 lookup 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.

@article{Theoryandapplicationsofthedoublebasenumbersystem,
title = {Theory and applications of the double-base number system},
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 lookup 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.},
url = {https://ieeexplore.ieee.org/document/805158},
year = 1999,
author = { V.S. Dimitrov and G.A. Jullien and W.C. Miller },
comment = {},
urldate = {2020-02-03},
collections = {basically-computer-science,easily-explained,integerology,unusual-arithmetic}
}