A 2-digit DBNS filter architecture

We have previously reported on a novel number representation using 2 bases which we refer to as the double-base number system (DBNS). Our preferred implementation uses the relatively prime bases {2,3}. If we allow the exponents of the bases to be arbitrarily large signed integers, then we can represent any real number to any arbitrary precision by a single digit DBNS representation. By representing the digit position by the exponent values, we generate a logarithmic-like representation which we can manipulate using an index calculus. A multiplier accumulator architecture for a FIR filter application has been reported which uses a half-index domain to remove the problem of addition within the index calculus. In this paper we show that using a 2-digit DBNS representation for both the input data and the filter coefficients can result in substantial hardware savings compared to both the single-digit a DBNS approach and an equivalent binary implementation of a general multiplier accumulator. In the paper we discuss the filter architecture, techniques for converting between binary and the 2-digit DBNS representations, and also the design technique used to generate the 2-digit DBNS FIR filter coefficients.