A.A. Kolyada - Dr.Sc. (Phys.-Math.), Associate Professor, Main Research Scientist, Laboratory of Specialized Computer Systems, A.N. Sevchenko Institute of Applied Physical Problems of Belarusian State University, Minsk, Belarus. E-mail: razan@tut.by
P.V. Kuchynski - Dr.Sc. (Phys.-Math.), Associate Professor, Head of A.N. Sevchenko Institute of Applied Physical Problems of Belarusian State University, Minsk, Belarus. E-mail: niipfp@bsu.by
A.F. Chernyavsky - Dr.Sc. (Eng.), Professor, Head of the Department of Informatics, A.N. Sevchenko Institute of Applied Physical Problems of Belarusian State University, Minsk, Belarus. E-mail: achern@bsu.by

Basic principles of the range-index technology of the synthesis of algorithms aimed to conversion from minimally redundant modular representation to positional representation are expounded. Proposed algorithms are based on the direct realization of interval-modular numbers representation with using of the interval index, which has the simplest structure. A novel parallel technique of modular-positional conversion is described. The efficiency of the proposed approach is evaluated. Based on the established method and table-summation computing technology synthesized a new parallel algorithm for the reverse conversion.