residue number system (rns) is a non-weighted number system for integer number arithmetic, which is based on the residues of a number to a certain set of numbers called module set. the main characteristics and advantage of residue number system is reducing carry propagation in calculations. the elimination of carry propagation leads to the possibility of maximizing parallel processing and reduc...

signed digit (sd) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. such carry-free addition is primarily a three-step process; adding the equally weighted sds to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the transfers to...

This paper unifies the representations of different kinds of computer arithmetic. It is motivated by ideas developed in the book The End of Error by John Gustafson [5]. Here interval arithmetic just deals with connected sets of real numbers. These can be closed, open, half-open, bounded or unbounded. The first chapter gives a brief informal review of computer arithmetic from early floating-poin...