Adding flexibility to hybrid number systems

Hybrid Number systems (HNS's) represent a natural generalization of weighted and residue number systems. In HNS's, an integer is represented by using both weighted and residue notations; their arithmetic properties, wich have been investigated in depth, are strongly dependent on the ratio of the residue to weighted range of the representation. It is immediate that the ability of varying the residue-to-weighted-range ratio should enable to optimize the arithmetic performances of these systems. This paper shows that adding flexibility to hybrid systems is very simple and is equivalent to perform a number system conversion. A general procedure is proposed whose complexity is the same of the well known mixed radix converting algorithm. A VLSI architecture is presented and its area-time performances are evaluated according to VLSI theory assumptions.