Theory and applications of the double-base number system

In this paper, we analyze some of the main properties of a double base number system, using bases 2 and 3; in particular, we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus for logarithmic-like arithmetic with considerable hardware reductions in lookup table size. We discuss the application of this number system in the area of digital signal processing; we illustrate the discussion with examples of finite impulse response filtering.