Fixed point unsigned fractional representation in residue number system

Representing fractions is one of the fundamental problems in the Residue Number System (RNS) which is considered an integer number system with no fractional representation. This is one of its main drawbacks and one of the main obstacles in its widespread. In this paper a method for representing fractions in RNS is developed. The addition of fractions is easily implemented using this method. The multiplication operation is also implemented, but of course with more sophisticated procedures relative to the addition operation. The choice of the way to represent a fraction in accordance with this new method is determined using two criteria, the Uniqueness Criterion (UC) and the Precision Criterion (PC). Real numbers representation is also introduced and analyzed. The general equation for real number multiplication which can be considered as the most difficult one in this paper, is introduced