Binary-to-Multidigit Multidimensional Logarithmic Number System Conversion
Vassil Dimitrov, Graham Jullien, Roberto Muscedere · 2017
This chapter explores several hardware realizable techniques for converting a binary representation into a two-dimensional logarithmic number system two-dimensional logarithmic number system (2DLNS) representation. The techniques are based on the reversal of the multidimensional logarithmic number system (MDLNS)-to-binary converter. Since the table method for converting single-digit 2DLNS to binary is quite fast and can be implemented efficiently in hardware, it is only logical to try to reverse this process, i.e., to convert a binary two&s;s complement representation to a single-digit 2DLNS. The input to the single-digit 2DLNS to binary lookup table (LUT) is the second base exponent, b , and the outputs are the mantissa and the exponent. To reverse the process, the input to the LUT is the mantissa, M(b). . The chapter discusses the design of a novel conversion LUT with table size O(2 R ). In this approach author changes the address decode system from exact matching to range matching. They refer this as a range-addressable LUT (RALUT).