Representation of numbers in nonclassical numeration systems

Author

Frougny, Christiane

Author_Institution

Paris 8 Univ., France

fYear

1991

fDate

26-28 Jun 1991

Firstpage

17

Lastpage

21

Abstract

Numeration systems, the bases of which are defined by a linear recurrence with integer coefficients, are considered. Conditions on the recurrence are given under which the function of normalization which transforms any representation of an integer into the normal one-obtained by the usual algorithm-can be realized by a finite automaton. Addition is a particular case of normalization. The same questions are discussed for the representation of real numbers in basis θ, where θ is a real number >1. In particular it is shown that, if θ is a Pisot number, then the normalization and the addition in basis θ are computable by a finite automaton

Keywords

digital arithmetic; finite automata; number theory; Pisot number; addition; basis &thetas;; finite automaton; integer coefficients; linear recurrence; nonclassical numeration systems; normalization; number representation; real numbers; Acceleration; Automata; Character generation; Codes; Computational modeling; Computer science; Digital arithmetic; Modular construction; Parallel architectures; Polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic, 1991. Proceedings., 10th IEEE Symposium on

Conference_Location

Grenoble

Print_ISBN

0-8186-9151-4

Type

conf

DOI

10.1109/ARITH.1991.145528

Filename

145528