Implementing DBNS Arithmetic
Vassil Dimitrov, Graham Jullien, Roberto Muscedere · 2017
This chapter introduces the concept of representing numbers over two bases, rather than the ubiquitous single-base (single-radix) positional number representation. It also introduces basic methods for addition and multiplication using the tabular approach with substitution rules. The chapter discusses the implementation of arithmetic using the two-dimensional tabular representation, and the reduction rules. In particular, the use of Cellular neural networks (CNNs) to perform image morphology processing, such as pixel dilation and erosion, appeared to be perfectly suited to the problem of reduction of nonzero digits in two-dimensional double-base number system (DBNS) maps. The filter design algorithm optimizes the design using the multiplier-free constraint so as to mitigate the heavy quantization effect of using such a reduced representation. We should be able to modify such design approaches to include single-digit DBNS multiplier constraints. The extra dimension of the DBNS representation will provide a more flexible set of possible multipliers, with the ability to achieve better multiplier-free designs.