Different kinds of computer arithmetic follow an abstract mathematical pattern and are just special realizations of it. The basic mathematical concepts are sketched here. The concepts of rounding, of a screen, and of rounded arithmetic operations are defined in an axiomatic manner fully independent of special data formats and encodings. These abstract concepts are then applied and illustrated b...

COMPUTER arithmetic is a field that encompasses the definition and standardization of arithmetic system for computers. The field also deals with issues of hardware and software implementations and their subsequent testing and verification. Many practitioners of the field also focus on the art and science of using computer arithmetic to carry out scientific and engineering computations. Computer...

A novel system for representing the rational numbers based on Hensel's p-adic arithmetic is proposed. The new scheme uses a compact variable-length encoding that may be viewed as a generalization of radix complement notation. It allows exact arithmetic, and approximate arithmetic under programmer control. It is superior to existing coding methods because the arithmetic operations take particula...

We present a transformation rule to convert linear codes into arithmetic codes. Linear codes are usually used for error detection and correction in broadcast and storage systems. In contrast, arithmetic codes are very suitable for protection of software processing in computer systems. This paper shows how to transform linear codes protecting the data stored in a computer system into arithmetic ...

Computer arithmetic is the logical theory which formalizes the way computers manipulate integer numbers. In this paper, we describe a combined system whose components are a logical theory for the Isabelle theorem prover, a calculational engine based on rewriting techniques, and a decision procedure for an extension of quantiier-free Presburger arithmetic. The goal of this work is to provide a g...

In the study of long-time correlations extremely long orbits must be calculated. This may be accomplished much more reliably using fixed-point arithmetic. Use of this arithmetic on the Cray–1 computer is illustrated.

The purpose of this master's thesis was to explore the circuit design space (speed, area, power) of conventional binary arithmetic and to suggest improvements or alternatives to this arithmetic. The alternatives to the binary arithmetic focused on was the Signed-Digit (SD) number system, the Residue Number System (RNS) and the combination of these two systems (RNS+SD). The work resulted in new ...

This paper proposes the use of level-index (LI) and symmetric level-index (SLI) computer arithmetic for practical computation with error bounds. Comparisons are made with oating-point and several advantages are identiied.

In this paper, we discuss arithmetic structures based on quantum cellular automata (QCA). By taking advantage of the unique capabilities of QCA we are able to design interesting computational architectures. We describe important design considerations and show how addition and multiplication circuits can be implemented using QCADesigner, a QCA design tool which has been developed in our laborato...

Given a computer-based instructional program and a school in which to work, it is possible to supplement or enrich the teacher’s instruction by taking over the more routine daily tasks, presenting special materials, or giving the daily lesson itself. The task of the present project was to prepare a program in arithmetic t o review and teach the basic number facts as a supplement to the teacher...