The main principles of the Fibonacci computer design

Problem of the fault-tolerant computers. The modern computer science comes to comprehension of principal lack of the digital information processing from the point of view of a higher reliability assurance. In this connection remarks of the famous West computer specialists B. Litlwood and L. Strigini seem to be highly interesting:

"The same nature of the digital electronic devices prevents elaborating the absolute reliable programmed products. Many physical systems are essentially continuous and can be described by the "smooth" mathematical functions. In so doing the small input change brings into the small output change. Quite the contrary the smallest possible perturbation of the computer state (for example, the exchange of the bit 0 by the bit 1) can bring into the radical change of the applied solution".

It was determined that just the failure of the control computer of the rocket "Atlas" that carried the first American cosmic station "Mariner -1" made the rocket deviate from the true course. As the result the rocket and cosmic station were destroyed. This example shows that the mankind become the 'hostage" of the computer faults and failures.

That is why the main direction of modern computer development is the fault-tolerant computer design. The central idea of the fault-tolerant computers is an introduction of the hardware and code redundancy permitting to detect the faults and failures arising within the computer circuits. The traditional solution consists of introduction of the redundancy into the computer after when the number system is chosen. However the simplest idea is introducing the code redundancy into computer at the number system choice. It is just this background underlied the Fibonacci computers. Hence the main purpose of the Fibonacci computer is the high reliability assurance of the information processing by using the redundancy of the Fibonacci and "Golden" codes.

Advantages of the ternary mirror-symmetrical number system. Many different number systems with irrational radixes have been considered at the pages of our Museum. The majority of them first of all is of theoretical interest. Comparing the different Fibonacci number systems for the practical realization of the Fibonacci computer from the technical point of view, one may give the decisive preference to the "golden" mirror-symmetrical number system. And we would emphasize these advantages.

The ternary mirror-symmetrical number system is the result of the long historical development of number system and is the joining the positional principle of number representation (Babylon, 2000 B.C.), the ternary symmetrical number system with numerals {`1, 0, 1} (Fibonacci, 13 c.) and the number system with an irrational base (Bergman, 1957).

    This unique combination caused the creation of the new number system with unique mathematical and technical properties, namely:
  1. Being the positional number system, the mirror-symmetrical number system saves all the well-known mathematical advantages of the classical positional number systems, in particular the binary number system.
  2. Being the symmetrical number system with numerals {`1, 0, 1}, the mirror-symmetrical number system has the important arithmetical advantage in comparison with the classical binary number system. This one allows representing the negative and positive numbers in the "direct" code and performing the arithmetical operations over them in the "direct" code without preliminary comparison by the value. It simplifies the computer arithmetical structures and can raise the speed acting of processors.
  3. Being the number system with irrational radix and representing the integers as the end sums of the golden ratio powers, it brings into the discovery of the new fundamental mathematical property of integers arising at their representation in the ternary "golden" code. This property is called the mirror-symmetrical property and consists of the fact that the left-hand part of the code representation is mirror-symmetrical to its right-hand part regarding to the 0-th digit. The mirror-symmetrical property is the invariant regarding to the arithmetical operations and plays a role of the main checking principle of the ternary mirror-symmetrical computer.

Thus we have finished the consideration of one of the modern mathematical discoveries in number system theory. And what is the attitude of modern science and mathematics to this discovery? We will tell about this at the next pages of our Museum. Follow us!