Method for performing the operation of adding the remainder of numbers modulo

One of the components of a computer system (CS) in a positional binary number system (PNS) is an adder of two numbers. In particular, adders modulo mi of two numbers are also components of the CS. This type of modulo adders is widely used both in the PNS and in the non-positional number system in the residual classes (RNS). An important and urgent scientific and applied problem is the problem of constructing the adders, which operate by modulus mi, that is an arbitrary RNS modulo. If the remainders ai and bi of both numbers A and B in RNS are represented in a binary PNS, then the adder of two residuals ai and bi by modulus mi is a sequential set of n binary one-bit adders (BOBA). The purpose of the article is to develop a method for performing the operation of modular addition (ai + bi)mod mi of two remainders of numbers by an arbitrary modulo mi based on the use of a positional binary adder modulo M = 2n - 1. The proposed method is based on the use of the well-known structure of positional binary adders modulo M = 2n - 1. Technically, the problem of creating the structure of the modular adder is formulated as follows. It is necessary to provide conditions under which the initial adder in PNS modulo M performs the addition operation modulo mi. This procedure is carried out by introducing additional connections as X¯i­j in the positional adder modulo M = 2n - 1, where the expression X¯i­j denotes one-way connection between the output of the j-th BOBA and the input of the i-th BOBA.