Abstract
The paper considers the operation of summation of binary codes in the scheme of a multi digit parallel adder without carry. The process of the operation of summation uses a pairing algorithm that provides for a logarithmic complexity to the algorithm of the calculation in the adder’s scheme. Since the codes for the operation of summation, known in the literature, such as Galois field codes, the XAND codes, are defined by the systems of recurrent codes that contain one of the initial codes of complete combinatorial system with repetition, then the given codes are a particular case of the class of combinatorial systems of binary codes with a ring structure and initial code of complete combinatorial system with repetition. Therefore, the only basis of the mentioned systems of binary codes indicates the usefulness of their classification generalization, within the framework of the operation of summation, on the basis of a single criterion – an object of binary codes. Thus, the generalization of the classification of binary codes simplifies the structure of the subject area, increases the variety of systems of binary codes, in particular, for their application in arithmetic operations with binary numbers. It was established that the properties of the recurrent method of the synthesis of binary codes allow focusing the principle of building codes in the range of complete combinatorial system with repetition, which ensures reduction of the thesaurus of the parallel adder of binary codes without carry. The results of this study may be a component of the technology of designing electronic computing systems because: – they expand the apparatus of obtaining recurrent binary codes for their application in the information technology; – they provide a possibility to control the selection of the code at the stage of designing a computing device; – they help predict the impact of the implementation of the selected code for the solution of problems of the information systems.. – they minimize hardware costs associated with the selection of the system of binary code for the calculation.
Highlights
Since the use of binary codes for the operation of summation without carry is the task still unsolved, this paper demonstrates a new standard of the synthesis of binary codes, which comes down to that the set system of binary codes (instance of P(2, bi) of the class P(2, n)) is selected on the ring structure with the help of corresponding initial block of complete combinatorial system with repetition
It was established that the properties of recursive method of the synthesis of binary codes allow focusing the principle of building codes in the range of complete combinatorial system with repetition, which ensures reduction of the thesaurus of the parallel adder of binary codes without carry
It was found that the system of binary codes, formed by means of any initial code of complete combinatorial system with repetition, has a ring structure, which allows using any system of binary codes in the operation of adding codes without carry
Summary
Binary code is a general designation of the code, by which messages can be transmitted in sequences that have two characters (for example, “0” and “1”). The number of combinations (codes) of n-digit binary code is equal to the number of locations with repetition of n elements by m
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