A hybrid DBNS processor for DSP computation

This paper introduces a modification to an index calculus representation for the double-base number system (DBNS). The DBNS uses the bases 2 and 3; it is redundant (very sparse) and has a simple two-dimensional representation. An extremely sparse form of the DBNS uses a single non-zero digit to represent any real number with arbitrary precision. In this case the single digit can be identified by its coordinates (indices) in the two-dimensional representation space. The modification proposed in this paper, targeted to DSP inner product computations, uses a single digit representation for the coefficient vector and a 2-digit representation for the data vector. We show that a reduction of over 80% in hardware cost is possible using this hybrid representation compared to the original single-digit technique.