Weight-Based Sum Codes Apply Coefficients from Leading Digits with Which the Powers of Two Begin for Calculations Control Organization in Discrete Systems

We analyze the problem of organizing the control of calculations at the outputs of combinational logic circuits. A method of constructing a sum code based on preliminary weighting of data vector bits by weighting coefficients from a number of leading digits of powers of two (sequences A008952 from the N. J. A. Sloan encyclopedia) is presented. It is proposed to build a sum code when calculating the total weight of significant digits of the data vector in the ring of deductions modulo M=16. Such a code has 4 check bits and is comparable in redundancy with the known sum code of significant digits of the data vector in the ring of deductions modulo M=16, but has improved characteristics of error detection. In the paper it is proved that the considered method of code construction gives noise-resistant codes at any values of the number of data bits. In the course of the research the characteristics of error detection by the code proposed by the authors are established. In the experiment with combinational benchmarks, it is shown that the new sum code is much more efficient in detecting errors in data vectors than the classical modular sum code. For half of the benchmarks, it is obtained that the new code has less than 3 % of errors in the class of undetectable errors than the modular sum code. This indicates the high efficiency of using the code developed by the authors to organize the control of combinational logic devices. The paper also proposes a method of constructing a noise-resistant sum code in the ring of deductions by arbitrary module, which can also be used in solving similar problems. The results of the work may be of interest to developers of highly reliable and fault-tolerant discrete devices and systems.