RNS-based logarithmic adder

Abstract

The operation of logarithmic addition has always been burdened with large volumes of look-up tables. Therefore with a goal of reducing the ROM size required, an elegant and novel technique for logarithmic addition using the residue number system is demonstrated. To formulate this technique, the properties of finite fields and finite rings are exploited. A multiple-base logarithm is defined first, which is then successfully used for the formulation of the proposed technique for logarithmic addition. With this approach, the ROM requirement has been reduced to a bare minimum, thereby reducing the complexity of logarithmic addition, and permitting an elegant and efficient implementation.