The operation of logarithmic addition was always eclipsed with heavy volumes of look-up tables. So with a goal to reduce the ROM size, an elegant and novel technique for logarithmic addition using RNS (Residue Number System) is demonstrated in this paper. To formulate this technique, the properties of Finite Fields and Finite Rings are exploited. A multiple base logarithm has been defined first, which was then successfully used for the formulation of our proposed technique for logarithmic addition. With our approach, the ROM requirement has been reduced to a bare minimum, thereby reducing the complexity of logarithmic addition, enabling an elegant and efficient implementation. 1 Introduction Computing techniques based on logarithmic principles can simplify multiplication, division, roots and powers. When logarithms are used, multiplication and division are reduced to addition and subtraction respectively, and powers and roots are reduced to multiplication and division respectively. In contrast, addition and subtraction involve complicated operations and require prohibitively large ROM size [1]. Hence, it is of great interest to probe into the issues related to the reduction of ROM size. It is observed that RNS is the most appropriate choice to achieve the same. An RNS is defined by a set of relatively prime integers (moduli) , ,…, .
DIRECT ANALOG-TO-RESIDUE CONVERTERSThe design of residue converters is an important area of research among RNS based systems. Currently, an analog signal is first converted into binary and then to residue using a binary-to-residue converter. To overcome the inefficiencies due to this two step process, two novel approaches for the design of a direct analog-to-residue (A/R) converter are presented in this paper. They are based on the successive approximation as well as the flash conversion approach.In the former, two analog-to-digital ( A D ) converters are cascaded with minimal modifications providing a conversion speed very close to that of a conventional A/D converter. In the latter an iterative technique as well as the principle of subranging are successfully applied to generate the first residue. The remaining residues in both approaches are generated by adding a few modulo adders, and a small look-up table that uses only a very small percentage of the entire chip area.
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