The subject of the article is the study of the structure of low-bit binary adders for an arbitrary modulus of the residual class system (RCS). The purpose of this article is to develop an algorithm for synthesizing the structure of the adder of two residuals of numbers by an arbitrary value of the RCS module, by organizing inter-bit connections between the binary digits of the adder, the combination of which determines the structure of the adder modulo. Tasks: to investigate the possibility of performing the operation of addition of two residuals in RCS based on positional binary adders; to analyze the influence of additionally introduced interdigit connections into the positional binary adder on the value of the contents of this adder; to develop an algorithm for the synthesis of an adder by an arbitrary RCS module. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RCS. The following results were obtained. It is shown in the work that the introduction of additional interdigit connections in a positional binary adder allows changing the contents of this adder. The rules for the introduction of these additional links are formulated, on the basis of which an algorithm for the synthesis of an adder by an arbitrary RCS modulus is obtained. Specific examples of the synthesis of structures of binary adders for various values of the RCS modules are given. Conclusions. Thus, the paper proposes an algorithm for the synthesis of an adder by an arbitrary RCS module, which is based on the use of positional binary adders, by introducing additional inter-bit connections. The application of the considered algorithm expands the functionality of positional binary adders