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

页码：848 / 851

页数：4

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