Basic micro-operations
The basic idea of the self-checking processor design consists of the following. It is necessary to choose such a set of the micro-operations called the *convolution;**devolution;**replacement;**absorption.*
The first two micro-operations were considered above. The convolution and devolution are the following code transformations fulfilled over the next three digits in framework of the same Fibonacci code combination.
The micro-operation of is the two-placed micro-operation performed over the same digit of two registers, the top register of The micro-operation of the is also the two-placed micro-operation when the binary 1's of the It is necessary to attract attention to the following "technical" peculiarity of the above-considered basic micro-operations. For the register interpretation of these micro-operations each micro-operation may be performed by means of the inversion of the flip-flops involved in the micro-operation. It means that each micro-operation is reduced to the flip-flop switching.
Let's consider two binary combinations, which are in the registers of As the result of the "replacements" we get two new code combination The logical operation of In the above example we have fulfilled simultaneously all the possible micro-operations of the "replacement" and the "absorption" over the code combinations of The logical operation of the As the result we get the code combination
For example let's summarize the following Fibonacci representations:
The addition is over because all the binary 1's moved from the register
® 1 0 1 0 0 1 0 1 0 = 0 1A + B.Thus, the Fibonacci addition is reduced to the sequential fulfillment of the micro-operations of the "replacement" over the code combinations
Let's demonstrate the Fibonacci subtraction by using the following example. It is necessary to subtract the Fibonacci representation
The subtraction is over. After reducing the Fibonacci representation
The subtraction result is in the lower register
Note that the arithmetical operations of the And now we would like to comment the Fibonacci arithmetic based on the "basic micro-operations". We have proved that all the above-considered "basic micro-operations" possess "functional completeness", that is all the possible logical and arithmetical operations can be reduced to the "basic micro-operations". And therefore, we can design the Fibonacci processor and computer based on the "basic micro-operations". But what advantages will have such Fibonacci processor in comparison to the classical computers based on the classical "binary" number system? To answer the question we have to demonstrate the possibility to check errors in processors, which can arise in processor over influence of different internal and external factors. Follow us! |