ABSTRACT

This chapter provides an initial exploration of the multidimensional logarithmic number system (MDLNS). It also discusses the implementation of a systolic two-dimensional logarithmic number system (2DLNS) FIR filter, in which the advantages of easy multiplication within the representation are exploited. The conversions from 2DLNS to binary will still require a lookup table (LUT), but one that is much smaller than required for handling 2DLNS addition and subtraction. The LUT is used to convert the second base portion of the 2DLNS number into a binary representation. Therefore the size of the LUT is dependent on the number of bits used to represent the second base exponent. For small-input word lengths, a ROM LUT is probably the best approach in terms of hardware cost on silicon. The word length limit to this LUT approach depends on the technology, and we do have the advantage in forward conversion that only a single ROM is required to drive a potentially large computational array.