DocumentCode
1250035
Title
Closed-form expression for the average weight of signed-digit representations
Author
Wu, Huapeng ; Hasan, M. Anwar
Author_Institution
Dept. of Electr. & Comput. Eng., Illinois Inst. of Technol., Chicago, IL, USA
Volume
48
Issue
8
fYear
1999
fDate
8/1/1999 12:00:00 AM
Firstpage
848
Lastpage
851
Abstract
In radix-r number system, the minimal weight signed-digit (SD) representation has minimal number of nonzero signed-digits which belong to the set {±1, ±2, ..., ±(r-1)}. In this article, we derive closed form expressions for the average number of nonzero digits in the minimal weight SD representation and for the average length of the canonical SD representation, a special case of the minimal weight SD form, of a positive integer whose radix-r form is of length n, n⩾1
Keywords
digital arithmetic; average weight; canonical SD representation; closed form expressions; closed-form expression; minimal weight SD representation; minimal weight signed-digit representation; nonzero digits; nonzero signed-digits; positive integer; radix-r form; radix-r number system; signed-digit representations; Arithmetic; Closed-form solution; Elliptic curves; Probability distribution;
fLanguage
English
Journal_Title
Computers, IEEE Transactions on
Publisher
ieee
ISSN
0018-9340
Type
jour
DOI
10.1109/12.795126
Filename
795126
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