Hybrid number systems (HNSs) represent a natural generalisation of weighted and residue number systems. In HNSs, an integer is represented by using both weighted and residue notations; their mathematical properties, which have been investigated in depth, are strongly dependent on the ratio of the residue to the weighted range of the representation. It is apparent that varying the residue-to-weighted-range ratio should enable us to optimise the mathematical performances of these systems. This paper shows that adding flexibility to hybrid systems is very simple. A general procedure is proposed whose complexity is the same as the well-known mixed radix converting algorithm. A VLSI architecture is presented and its area-time performances are evaluated.
Adding Flexibility to Hybrid Number Systems
PINOTTI, Maria Cristina
1992
Abstract
Hybrid number systems (HNSs) represent a natural generalisation of weighted and residue number systems. In HNSs, an integer is represented by using both weighted and residue notations; their mathematical properties, which have been investigated in depth, are strongly dependent on the ratio of the residue to the weighted range of the representation. It is apparent that varying the residue-to-weighted-range ratio should enable us to optimise the mathematical performances of these systems. This paper shows that adding flexibility to hybrid systems is very simple. A general procedure is proposed whose complexity is the same as the well-known mixed radix converting algorithm. A VLSI architecture is presented and its area-time performances are evaluated.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
