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
相关论文
共 50 条
  • [1] SIGNED-DIGIT REPRESENTATIONS OF MINIMAL HAMMING WEIGHT
    ARNO, S
    WHEELER, FS
    IEEE TRANSACTIONS ON COMPUTERS, 1993, 42 (08) : 1007 - 1010
  • [2] MINIMUM WEIGHT MODIFIED SIGNED-DIGIT REPRESENTATIONS AND FAST EXPONENTIATION
    JEDWAB, J
    MITCHELL, CJ
    ELECTRONICS LETTERS, 1989, 25 (17) : 1171 - 1172
  • [3] BINARY SIGNED-DIGIT REPRESENTATIONS IN PAPERFOLDING
    Bates, Bruce
    Bunder, Martin
    Tognetti, Keith
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 106 (03) : 363 - 375
  • [4] Generation of signed-digit representations for integer multiplication
    Dempster, AG
    Macleod, MD
    IEEE SIGNAL PROCESSING LETTERS, 2004, 11 (08) : 663 - 665
  • [5] Arithmetic circuits combining residue and signed-digit representations
    Lindström, A
    Nordseth, M
    Bengtsson, L
    Omondi, A
    ADVANCES IN COMPUTER SYSTEMS ARCHITECTURE, 2003, 2823 : 246 - 257
  • [6] Optimal binary signed-digit representations of integers and the Stern polynomial
    Laura Monroe
    Designs, Codes and Cryptography, 2024, 92 : 1501 - 1516
  • [7] Optimal binary signed-digit representations of integers and the Stern polynomial
    Monroe, Laura
    DESIGNS CODES AND CRYPTOGRAPHY, 2024, 92 (06) : 1501 - 1516
  • [8] Fractional windows revisited:: Improved signed-digit representations for efficient exponentiation
    Möller, B
    INFORMATION SECURITY AND CRYPTOLOGY - ICISC 2004, 2004, 3506 : 137 - 153
  • [9] Closed-Form Representations of Friction
    Huang, Jin
    Li, Xingyu
    Li, Huiqian
    Chen, Ye-Hwa
    Zhong, Zhihua
    IEEE ACCESS, 2021, 9 : 31287 - 31296
  • [10] Digital filter design using subexpression elimination and all signed-digit representations
    Dempster, AG
    Macleod, MD
    2004 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOL 3, PROCEEDINGS, 2004, : 169 - 172
12345