Communications of the ACM
Structure of Computers and Computations
Structure of Computers and Computations
Overview of an Arithmetic Design System
DAC '81 Proceedings of the 18th Design Automation Conference
A suggested approach to computer arithmetic for designers of multi-valued logic processors
MVL '78 Proceedings of the eighth international symposium on Multiple-valued logic
A study of redundant number representations for parallel digital computers
A study of redundant number representations for parallel digital computers
Design of complex number digital arithmetic units based on a modified bi-imaginary number system.
Design of complex number digital arithmetic units based on a modified bi-imaginary number system.
Quantitative complexity analysis of finite number systems for customized arithmetic processors
Quantitative complexity analysis of finite number systems for customized arithmetic processors
Arithmetic Algorithms in a Negative Base
IEEE Transactions on Computers
Sign Detection in Residue Number Systems
IEEE Transactions on Computers
Arithmetic Algorithms in a Negative Base
IEEE Transactions on Computers
On the Use of Residue Arithmetic for Computation
IEEE Transactions on Computers
A multiprocessor system design
AFIPS '63 (Fall) Proceedings of the November 12-14, 1963, fall joint computer conference
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This paper describes aspects of an arithmetic design system (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. In computer arithmetic we are concerned with establishing a correspondence between abstract quantities (numbers) and some physical representation (symbols), and with simulating the operations on these symbols. The ADS is intended to help study the cost and performance of alternate simulations. A finite number system is a triple 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 its symbol set. A set of these digit vector algorithms are proposed for conducting arithmetic design. A number system matrix defines the digit vector algorithm for numerous number systems and a method for computing time and space complexity of compositions of these algorithms is proposed. An example of how the system could be used to compare addition, with and without out-of-range detection, for three number systems is given.