The Fibonacci "convolution" register As is mentioned above, the operations of the "convolution", the "devolution" and the "reducing to the minimal form" are the main operations of the Fibonacci arithmetic and the devices for their realization were the main topic of Fibonacci patenting abroad. And we consider at this page of our Museum the simplest electronic device for realization of the "convolution". As the basis of the "convolution" device one can chosen the classical binary register consisting of flip-flops. This register has the special logical circuits for the convolution fulfilment. Each digit of the register contains the binary flip-flop and the logical elements. The "convolution" (011 ® 100) may be presented as the inversion of the flip-flop states. The inversion of the flip-flop state is performed very easily for the flip-flop with the "adjusting" and "counting" inputs. One of the possible variants of the "convolution" register is shown in Fig. 1. The "convolution" register consists of the five The logical element Note that of all the elements The convolution register in Fig. 1 operates in the following way. The input code information is sent to the information inputs 1 - 5 of the convolution register and enters the
Let the initial slate of the "convolution" register be the following:
It is clear that the convolution condition holds good only for the 1-st, 2-d and 3-d digits. The first synchronization signal
Here the "convolution" condition holds good for the 3-d, 4-s and 5-th digits. The next synchronization signal
The convolution is over. The "convolution" register plays an important role in the Fibonacci processor as the self-checking device. Let's consider the "convolution" register in Fig.1 since this point of view. The outputs of the logical elements - The binary code combination written into "convolution" register has not the minimal form. It means that the convolution condition is valid even for the one triple of the neighbouring flip-flops of the "convolution" register. This causes the appearance of the logical 1 at the output of the corresponding element
*AND*. Hence in this case the appearance of the logical 1 at the check output of the convolution register indicates that the convolution process is not over. This means that we have a possibility to indicate the termination of the convolution process by means of observing the check output of the "convolution" register. - The appearance of the constant logical 1 at the check output is the indication of the fault in the convolution register. Hence the convolution register is the natural self-checking device.
It is interesting to emphasize that the circuit in Fig.1 is the unusual circuit. It was recognized as the "pioneer" invention in many countries including U.S.A., Japan, England, Germany, France and Canada. |