Analytical form of Garner’s method of basis extension of the residue number system

The basic methods of extension of the basis of the residue number system are analyzed, the analytical assessments of the apparatus expenses are received. The conclusion on higher efficiency of the classical variant of Garner’s method while apparatus operating in terms of apparatus and time expenses is made. In accordance with the existing algorithmic description the analytical form of Garner’s method is designed; it helps to simplify the synthesis of the numerators of the basis extension of the residue number system, in particular apparatus operations, due to the fact, that the algorithmic method is replaced with its recurrent formula. The comparison of the apparatus operations of the modules of the basis extension of the residue number system based on the proposed analytical form and Garner’s classical method showed the equivalence. It is proposed to use the analytical form of Garner’s method to carry out the transformation of the codes of the residue number system into the positional codes of the traditional number system. The effectiveness of this solution while apparatus operating is shown.