Logarithmic conversion by four partitioned hybrid-ROMs

The logarithmic number systems (LNS) have long been used in arithmetic to simplify processes such as: multiplication to addition, division to subtraction, and powers to multiplication, etc. A difficult problem may arise from the accuracy of conversion during the processing operations and a very large number of product terms should be generated if a look-up table is realized by a ROM. In some cases, it may be impossible to use such a large capacity ROM (say, 2²⁴×24) if no partitioned scheme is used. This paper presents a four-partition conversion scheme in order to be implemented by small sized ROMs. It can generate better results and higher speed conversion comparing with previous methods for two- or three-partition schemes. This algorithm can also be used in conversion of antilogarithms