Algorithm-based Study on Transformation Combination for Carry-free Modified Signed Digit(MSD) Addition

IF 3.7 3区计算机科学 Q2 COMPUTER SCIENCE, INFORMATION SYSTEMS Journal of Cloud Computing-Advances Systems and Applications Pub Date : 2023-07-01 DOI:10.1109/CSCloud-EdgeCom58631.2023.00058

Baofeng Qi, Shaojiang Sun, Yihui Tong, J. Zhang, Zhehe Wang, Xianchao Wang

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Abstract

Addition is the most basic operation in arithmetic. And the binary number system is used to implement the adder in modern electronic computer. The inherent properties of binary make it difficult to implement carry-free addition. And the redundancy of Modified Signed Digit(MSD) number system has been applied to implementing carry-free addition by use of four logic transformations. This paper explores in depth the reason why the MSD number system can be used to implement carry-free addition and obtain 16 pairs of transformation which can be used to implement MSD addition. Moreover, we obtain all transformation combinations for three-step MSD addition by designing relevant algorithms. Meanwhile, we find the test data set with minimum number of trits for MSD addition. Finally, to improve computational efficiency, we explore the optimal transformation combinations for implementation of MSD adder. And we find that there are four optimal transformation combinations, i.e. (5, 3, 0), (5, 3, 1), (10,2,0), and (10, 2, 4) which all use the same number of basic operating units(BOUs).

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基于算法的无携带修改符号数字加法变换组合研究

加法是算术中最基本的运算。在现代电子计算机中，加法器是用二进制来实现的。二进制的固有性质使其难以实现无进位加法。并利用修正符号数(MSD)数系统的冗余性，利用四种逻辑变换实现了无进位加法。本文深入探讨了MSD数制可用于实现无进位加法的原因，得到了可用于实现MSD加法的16对变换。此外，通过设计相关算法，得到了三步MSD加法的所有变换组合。同时，我们找到了用于MSD添加的最小特征的测试数据集。最后，为了提高计算效率，我们探索了实现MSD加法器的最佳变换组合。我们发现有四种最优变换组合，即(5,3,0)、(5,3,1)、(10,2,0)和(10,2,4)，它们都使用相同数量的基本操作单元(bou)。

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来源期刊

Journal of Cloud Computing-Advances Systems and Applications Computer Science-Computer Networks and Communications

CiteScore

6.80

自引率

7.50%

发文量

审稿时长

75 days

期刊介绍： The Journal of Cloud Computing: Advances, Systems and Applications (JoCCASA) will publish research articles on all aspects of Cloud Computing. Principally, articles will address topics that are core to Cloud Computing, focusing on the Cloud applications, the Cloud systems, and the advances that will lead to the Clouds of the future. Comprehensive review and survey articles that offer up new insights, and lay the foundations for further exploratory and experimental work, are also relevant.