<p>The relevance of developing methods and means for interbase conversion of multi-digit numbers represented in Rademacher binary codes, Rademacher–Christensen and Haar–Christensen residue codes of the residue class system (RCS) is substantiated. The aim of the research is to develop a method and algorithm for converting multi-digit numbers represented by Rademacher (R) basis binary codes into corresponding residue codes of the Rademacher–Christensen (R–C) and Haar–Christensen (H–C) bases. The mathematical foundations of the available algorithms and means of converting multi-digit binary R-codes into (R–C) and (H–C) residue codes are analyzed. As a result, it is proved that the basic components of mathematical operations for converting Rademacher basis binary R-codes into Christensen basis (R–C) and (H–C) residue codes are parallel operations of R-code convolution using a system of mutually prime RCS modules. A new method and algorithm for interbase conversion of multi-digit binary R-codes into (R–C) and (H–C) residue codes are proposed. Examples of implementing the proposed method and algorithm in the data encoding range within 32-bit binary codes are provided. The characteristics of parallelization and performance of addition and multiplication operations in (R–C) and (H–C) codes are analyzed. A software model for investigating and implementing interbase conversion of R-codes into (R–C) and (H–C) codes in the Python programming language has been constructed.</p>