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  • Abstract - Efficient Techniques for Binary-to-Multidigit Multidimensional Logarithmic Number System Conversion Using Range-Addressable Look-Up Tables
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Efficient Techniques for Binary-to-Multidigit Multidimensional Logarithmic Number System Conversion Using Range-Addressable Look-Up Tables
March 2005 (vol. 54 no. 3)
pp. 257-271
The Multidimensional Logarithmic Number System (MDLNS), which has similar properties to the classical Logarithmic Number System (LNS), provides more degrees of freedom than the LNS by virtue of having two, or more, orthogonal bases and has the ability to use multiple MDLNS components, or digits. Unlike the LNS, there is no monotonic relationship between standard binary representations and MDLNS representations. Using look-up tables (LUTs) to perform the mapping function can be unrealistic for hardware implementations when large binary ranges or multiple digits are used. This paper proposes a novel range-addressable technique for using look-up tables that allows efficient conversion from binary-to-single or multidigit MDLNS with varying accuracies, depending on the selected implementation.

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Index Terms:
Number representations, computer arithmetic, logarithmic number system, double-base number system, multidimensional logarithmic number system, binary-to-MDLNS conversion, range-addressable look-up tables.
Citation:
Roberto Muscedere, Vassil Dimitrov, Graham A. Jullien, William C. Miller, "Efficient Techniques for Binary-to-Multidigit Multidimensional Logarithmic Number System Conversion Using Range-Addressable Look-Up Tables," IEEE Transactions on Computers, vol. 54, no. 3, pp. 257-271, March 2005, doi:10.1109/TC.2005.48
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