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    National Tsing Hua University Institutional Repository > 電機資訊學院 > 電機資訊學院學士班 > 期刊論文 >  Asymmetric high-radix signed-digit number systems for carry-free addition

    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/42014

    Title: Asymmetric high-radix signed-digit number systems for carry-free addition
    Authors: Shieh, Shao-Hui;Wu, Cheng-Wen
    教師: 吳誠文
    Date: 2003
    Publisher: Institute of Information Science Academia Sinica
    Relation: JOURNAL OF INFORMATION SCIENCE AND ENGINEERING, Volume 19, Issue 6, Pages 1015-1039, NOV 2003
    Keywords: asymmetric high-radix signed-digit number
    computer arithmetic
    number system conversion
    redundant number system
    signed-digit numbers
    Abstract: © 2003 Institute of Information Science Academia Sinica - We propose an asymmetric high-radix signed-digit (AHSD) number system for fast binary addition, and show that the AHSD number system supports carry-free (CF) addition. The CF additions in AHSD, to be classified as quasi-closed and subclosed additions, use only one redundant digit for any radix r greater than or equal 2. Novel algorithms for constructing the three-stage CF adder (CFA) based on the AHSD number system are also presented. Moreover, if the radix is specified as r = 2m, where m is any positive integer, the binary-to-AHSD conversion can be done in constant time regardless of the word-length. Hence, the AHSD-to-binary conversion dominates the performance of an AHSD-based arithmetic system. We also propose two efficient algorithms for converting AHSD numbers to binary format. The first uses a novel structure to achieve high speed, while the second uses simple transformations and conventional additions to provide hardware reusability. These results are important since the conversion from AHSD numbers to binary format has been considered the performance bottleneck of AHSD-based arithmetic systems.
    URI: JOURNAL OF INFORMATION SCIENCE AND ENGINEERING, Volume: 19, Issue: 6, Pages: 1015-1039, NOV 2003
    Appears in Collections:[電機資訊學院學士班] 期刊論文

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