Posibits, negabits, and their mixed use in efficient realization of arithmetic algorithms

G. Jaberipur, B. Parhami
{"title":"Posibits, negabits, and their mixed use in efficient realization of arithmetic algorithms","authors":"G. Jaberipur, B. Parhami","doi":"10.1109/CADS.2010.5623646","DOIUrl":null,"url":null,"abstract":"Positively weighted and negatively weighted bits (posibits, negabits) have been used in the interpretation of 2's-complement, negative-radix, and binary signed-digit number representation schemes as a way of facilitating the development of efficient arithmetic algorithms for various application domains. In this paper, we show that a more general view of posibits and negabits, along with their mixed use in any combination (using inverse encoding for negabits), unifies a number of diverse implementation schemes, while at the same time making the resultant designs more efficient by avoiding custom or modified hardware elements and restricting the implementation to the use of standard arithmetic cells. Such standard cells have been highly optimized and are continually improving due to their wide applicability. Other practical benefits of our formulation include facilitation of low-voltage and low-power design, again due to the widespread availability of standard cells in variants optimized for low-voltage operation or energy economy. Pedagogical benefits include more intuitive explanations for a number of widely used transformations, such as Booth's recoding and column compression.","PeriodicalId":145317,"journal":{"name":"2010 15th CSI International Symposium on Computer Architecture and Digital Systems","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 15th CSI International Symposium on Computer Architecture and Digital Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CADS.2010.5623646","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7

Abstract

Positively weighted and negatively weighted bits (posibits, negabits) have been used in the interpretation of 2's-complement, negative-radix, and binary signed-digit number representation schemes as a way of facilitating the development of efficient arithmetic algorithms for various application domains. In this paper, we show that a more general view of posibits and negabits, along with their mixed use in any combination (using inverse encoding for negabits), unifies a number of diverse implementation schemes, while at the same time making the resultant designs more efficient by avoiding custom or modified hardware elements and restricting the implementation to the use of standard arithmetic cells. Such standard cells have been highly optimized and are continually improving due to their wide applicability. Other practical benefits of our formulation include facilitation of low-voltage and low-power design, again due to the widespread availability of standard cells in variants optimized for low-voltage operation or energy economy. Pedagogical benefits include more intuitive explanations for a number of widely used transformations, such as Booth's recoding and column compression.
正位,负位,以及它们在有效实现算术算法中的混合使用
正加权和负加权比特(正比特、负比特)已被用于解释2补码、负基数和二进制符号数字表示方案,作为促进各种应用领域高效算术算法开发的一种方式。在本文中,我们展示了正位和负位的更一般的观点,以及它们在任何组合中的混合使用(对负位使用逆编码),统一了许多不同的实现方案,同时通过避免定制或修改硬件元素并限制实现使用标准算术单元使结果设计更有效。由于其广泛的适用性,这种标准电池已经得到了高度优化并不断改进。我们配方的其他实际好处包括促进低压和低功耗设计,这也是由于标准电池在低压操作或能源经济优化变体中的广泛可用性。教学方面的好处包括对许多广泛使用的转换的更直观的解释,例如Booth的重新编码和列压缩。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信