Overview of an Arithmetic Design System

This paper describes an evolving Arithmetic Design System (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. A finite number system is a tuple consisting of a symbol set (elements are called "digit-vectors"), an interpretation set, a mapping between these two sets, and a set of operators ("digit-vector algorithms") defined on the symbol set. A set of these digit vector algorithms are proposed for conducting arithmetic design and for computing time and space complexity of compositions of these algorithms. Once a transition has been made from arithmetic design to logic design, a sub-system of the ADS provides a estimate of time and space complexity with respect to a PLA-base of implementation.