ABSTRACT
This chapter introduces the Double-Base Number System (DBNS). Vassil Dimitrov introduced the technique to the author's research group (VLSI Research Group) at the University of Windsor in Ontario, Canada, in 1995. The main interest of the group was in digital signal processing (DSP) at that time, and so the author started to look at the application of DBNS representations to filter architectures. The near-canonic double-base representation (NCDBNR) seems to be a sufficiently sparse DBNS representation, but the sparseness soon disappears once the author starts to manipulate pairs of numbers when performing arithmetic of addition and multiplication. Canonic forms for DBNS representations are shown to be very sparse, and even though it is a computationally hard problem to find canonic representations, a simple greedy algorithm, with an expansion of sublinear length, is demonstrated to produce near-canonic representations, which can also be very sparse.
