Showing papers on "Residue number system published in 1973"

General Division in the Symmetric Residue Number System

Abstract: In the residue number system, the arithmetic operations of addition, subtraction, and multiplication are executed in the same period of time without the need for interpositional carry. There is a hope for high-speed operation if residue arithmetic is used for digital computation. The division process, which is one of the difficulties of this operation, is developed in the symmetric residue number system. The method described here is iterative in nature and requires the availability of two tables of the symmetric residue representations of a certain kind of integer. An algorithm for general division is derived, and the way of choosing the entries which are used to find a quotient is discussed.

A Study of Arithmetic Algorithms for a Residue Arithmetic Associative Processor.

Abstract: : The paper examines the concept of an associative processor whose arithmetic operations are based on residue arithmetic computations. Particular emphasis has been placed on the development and evaluation of arithmetic algorithms. Preliminary solutions are presented in a number of problem areas. One of the main results is that a residue arithmetic associative processor (RAAP) offers potentially large speedup in multiplication time over conventional associative processors. Improvement factors tabulated over a wide range of input bit lengths and epth of associativity are presented for various arithmetic algorithms. Interesting arithmetic problems such as input/output conversions and addition and multiplication algorithms are treated. The processor architecture for system control of a large number of residue fields is examined. Considerations of microprogramming arithmetic algorithms in the RAAP are described. (Modified author abstract)