High speed method of conversion numbers from residue number system to positional notation

The Residue Number System is a widely used non-positional number system. Residue Number System can be effectively used in applications and systems with a predominant proportion of addition, subtraction and multiplication operations, due to the parallel execution of operations and the absence of inter-bit carries. The reverse conversion of a number from Residue Number System to positional notation requires the use of special algorithms. The main focus of this article lies in introducing the new conversion method, which incorporates Chinese Remainder Theorem, Akushsky Core Function and rank of number. The step-by-step procedure of the conversion process is detailed, accompanied by numerical examples. The proof of the relationship between the ranks of positional characteristics using the Chinese Remainder Theorem is presented. Through careful analysis and comparison with existing transformation methods, it is concluded that the presented approach takes on average 8% less time than the Approximate Method.