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The authors analyze the process of transmission of discrete messages in a residue number system, i.e., the efficiency of the representation of decimal numbers in a residue number system for different values ​​of the module, that is. It is noted that it is characteristic of modern   information transmission systems that the information is contained in the information parameter at a fixed interval of the Nyquist element. The increase in the capacity is achieved by increasing the number of states of the information parameter in this interval, i.e., the number of different amplitudes, phases and frequencies of the carrier oscillation. In addition, using a residue number system when representing decimal numbers, the sum of the digits of individual numbers in most cases is less than 10 (except for the number N104) and an increase in the probability of not using moduli Е 3; 5; 7 leads to an increase in the entropy of the corresponding events.

Efficiency of transmission of discrete messages in a residue number system