Theory and applications of the double-base number system

• Published in 1999
• Added on 2020-02-03

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.

Links

• https://ieeexplore.ieee.org/document/805158

Other information

BibTeX entry

@article{Theoryandapplicationsofthedoublebasenumbersystem,
	key = {Theoryandapplicationsofthedoublebasenumbersystem},
	type = {article},
	title = {Theory and applications of the double-base number system},
	author = { V.S. Dimitrov and G.A. Jullien and W.C. Miller },
	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.},
	comment = {},
	date_added = {2020-02-03},
	date_published = {1999-09-26},
	urls = {https://ieeexplore.ieee.org/document/805158},
	collections = {Basically computer science,Easily explained,Integerology,Unusual arithmetic},
	url = {https://ieeexplore.ieee.org/document/805158},
	year = 1999,
	urldate = {2020-02-03}
}