Efficient conversion from binary to multi-digit multi-dimensional logarithmic number systems using arrays of range addressable look-up tables

Abstract

The multi-dimensional logarithmic number system (MDLNS), with similar properties to the logarithmic number system (LNS), provides more degrees of freedom than the LNS by virtue of having two orthogonal bases and the ability to use multiple digits. Unlike the LNS, there is no direct functional relationship between binary/floating point representation and the MDLNS representation. Traditionally look-up tables (LUTs) were used to move from the binary domain to the MDLNS domain. This method can be unrealistic for hardware implementation when large binary ranges or multiple digits are used. This paper introduces a range addressable technique for table look-up arrays that allows efficient conversion from binary to single or multi-digit MDLNS.