Non-Standard Numeration Systems
نویسندگان
چکیده
منابع مشابه
Parallel addition in non-standard numeration systems
We consider numeration systems where digits are integers and the base is an algebraic number β such that |β| > 1 and β satisfies a polynomial where one coefficient is dominant in a certain sense. For this class of bases β, we can find an alphabet of signed-digits on which addition is realizable by a parallel algorithm in constant time. This algorithm is a kind of generalization of the one of Av...
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Parallel addition in integer base is used for speeding up multiplication and division algorithms. k-block parallel addition has been introduced by Kornerup in [14]: instead of manipulating single digits, one works with blocks of fixed length k. The aim of this paper is to investigate how such notion influences the relationship between the base and the cardinality of the alphabet allowing block ...
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We study parallel algorithms for addition of numbers having finite representation in a positional numeration system defined by a base β in C and a finite digit set A of contiguous integers containing 0. For a fixed base β, we focus on the question of the size of the alphabet that permits addition in constant time, independently of the length of representation of the summands. We produce lower b...
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ژورنال
عنوان ژورنال: Acta Polytechnica
سال: 2005
ISSN: 1805-2363,1210-2709
DOI: 10.14311/762