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 look-up table size. We discuss the application of this new number system in the area of digital signal processing; we illustrate the discussion with examples of finite impulse response filtering.