The concept of a programmable multipurpose computation module for residue arithmetic is introduced. A possible design for the module is also presented. The application of the computation module in mathematical computation, coding, decoding, and scaling is demonstrated. Very high throughput rate is achieved by the use of parallel computation structures and pipelining of sequential operations.

Many ambitious computer algebra systems were initially designed in a flush of enthusiasm, with the goal of automating any symbolic mathematical manipulation “correctly.” Historically, this approach resulted in programs that implicitly used certain identities to simplify expressions. These identities, which very likely seemed universally true to the programmers in the heat of writing the CAS, (a...

We will first see how to convert a real number in binary form into its decimal equivalent. The key idea is that the binary digits to the left of the binary decimal point increase in factors of 2 for each place moved over. Similarly, the digits to the right of the binary decimal point decrease in factors of 2 for each place moved over. Consider the real number (101.1)2 in binary form. We have (1...

Many ambitious computer algebra systems were initially designed in a flush of enthusiasm, with the goal of automating any symbolic mathematical manipulation “correctly.” We see this kind of goal in programs like Macsyma, Maple, Mathematica. This approach often resulted in programs that implicitly used certain identities to simplify expressions. These identities, which likely seemed universally ...

COMPUTER arithmetic is one of the oldest research topics. Early civilizations used marked bones to memorize numerical values. This approach can be viewed as a combination of read only memories and a unary number system in which addition was very efficient. Around 3300 BC, the first true number systems appeared when Sumerian clay tablets were used to implement a radix-60 number system. A variati...

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis world in Pythagorean manner. unifies foundations mathematics (Peano and set theory), physics (quantum mechanics information), philosophical transcendentalism (Husserl’s phenomenology) into formal theory mathematical structure literally following Husserl’s tracе “philosophy rigorous science”. In pathway to ...

In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for...

This paper considers the role of dynamic aspects of mathematics specifically focusing on the calculus, including both physical human action and computer software that responds to physical action to produce dynamic visual effects. The development builds from dynamic human embodiment, uses arithmetic calculations in computer software to calculate 'good enough' values of required quantities and al...

Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...