Efficient techniques for binary-to-multidigit multidimensional logarithmic number system conversion using range-addressable look-up tables

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 work 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.