Shevchenko M. Models and method of binary binomial numbers arithmetic addition in information-communication technologies

The dissertation solves the following scientific and applied problem: the development and research of the arithmetic addition of binary binomial numbers with restrictions on the amount of software and/or hardware expenses in order to speed up the computational processing of binomial numerical information for more effective implementation of information and communication technologies for solving specialized tasks of information compression, generation combinatorial objects, combinatorial optimization, encryption, etc. The structural binary binomial number systems occupy a special place among heterogeneous number systems thanks to their significant redundancy, complex functional dependence between weight coefficients and values of binomial digits, similarity their structure to structure of the spread well-known code-combinations. But in the present time the developed rules and procedures to fulfil arithmetic operations on the binomial numbers, including the binomial addition, don’t exist. As a consequence, there is a restraining factor for embedding binomial number systems into information technologies devoted to data processing more widely. The aim of the dissertation devoted to research and development the models and method of arithmetic addition for binary binomial numbers that are generated with binary binomial number systems is to decrease time of this operation subject to restrictions on the amount of software and/or hardware expenses. The relevance of dissertation researches is defined by the fact that the models and method of binomial arithmetic addition development will become the basis for building binomial machine arithmetic into computer systems and components, will give new possibilities to create effective information and communication technologies of data processing such as combinatory objects generation, combinatory optimization, support of noise-immunity binomial computations, as well to stimulate further development of binomial number systems theory. The new scientific result of the dissertation is the decision of the important and relevant scientific and applied problem devoted to development of the models and method of binomial arithmetic addition that give a possibility to reduce time expenses required to implement the operation on binary binomial number systems with restrictions on the amount of hard and/or software expenses. The developed method of arithmetic addition for binary binomial numbers that conducts the addition of binary binomial numbers by processing cells coordinates of the addition matrix instead of processing values of the binomial coefficients on basis of carry, shift, symmetry and decomposition transformations. It requires much less the amounts of time and hardware and software expenses for obtaining the addition result in comparison with other being methods. The theory of binomial number systems and positional binomial count get further development that gives an additional impact to wider using binary binomial number systems and generated by them binomial numbers when developing new information technologies of data processing. The practical significance of the obtained results is determined by the developed algorithms of arithmetic addition for binary binomial numbers that are characterized efficiency, finiteness and that fact is they can be put into practice enough easily in terms of computational complexity.