Pipelined computation of LNS addition/subtraction with very small lookup tables

Abstract

Logarithmic number system (LNS) has the advantages of regular data flow high speed, and high precision. However, the development of LNS arithmetic is hindered by the large size of the lookup tables used in LNS addition/subtraction, since the size is exponentially proportional to the word length of the operands. To overcome this large-table problem, LNS addition/subtraction is proposed to be computed in a pipelined manner. The computation includes an exponential stage and a logarithmic stage. The exponential stage is implemented by using digit-parallel additive normalization and the logarithmic stage is implemented by using digit on-line multiplicative normalization. It has been computed that the size of the lookup tables used in a 33-bit LNS unit is about 0.543 Mbits, which is very small. The hardware cost of the other circuits in this LNS unit is only linearly proportional to the word length of the operands. We conclude that the proposed method makes large word-length LNS arithmetic possible.