Baofeng Qi, Shaojiang Sun, Yihui Tong, J. Zhang, Zhehe Wang, Xianchao Wang
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Algorithm-based Study on Transformation Combination for Carry-free Modified Signed Digit(MSD) Addition
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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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.
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