Closed-form expression for the average weight of signed-digit representations

被引：6
|
作者：
Wu, HP [1 ]
Hasan, MA
机构：
[1] IIT, Dept Elect & Comp Engn, Chicago, IL 60616 USA
[2] Univ Waterloo, Dept Elect & Comp Engn, Waterloo, ON N2L 3G1, Canada
来源：
IEEE TRANSACTIONS ON COMPUTERS | 1999年 / 48卷 / 08期
基金：
加拿大自然科学与工程研究理事会;
关键词：
radix-r number system; minimal weight signed-digit representation; canonical signed-digit representation;
D O I：
10.1109/12.795126
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
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 greater than or equal to 1.
引用
收藏
页码：848 / 851
页数：4
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