Low-precision Logarithmic Number Systems

Logarithmic number systems (LNS) are used to represent real numbers in many applications using a constant base raised fixed-point exponent making its distribution exponential. This greatly simplifies hardware multiply, divide, and square root. LNS with base-2 is most common, but this article, we show that for low-precision the choice of has significant impact. We make four main contributions. First, not closed under addition subtraction, so result approximate. choosing suitable can manipulate reduce average error. Second, subtraction be implemented efficiently logic rather than commonly ROM lookup tables, complexity which reduced by an appropriate base. A similar effect shown where arithmetic greater precision input. Third, input data from external sources expected LNS, conversion error selecting match Thus, there no one gives global optimum, selection trade-off between different factors. Fourth, circuits realized require lower area power consumption short word lengths.