Generalized matrix method for efficient residue to decimal conversion

In this paper, we present a matrix based method for efficient Residue to decimal conversion. First, we generalize a previously proposed technique that was restricted to 5-moduli set such that it becomes applicable to any RNS with the set of relatively prime integer moduli {m_i}_i=1,n. Next, we simplify the computing procedure by maximizing the utilization of the modulo-m_i adders and multipliers present in the RNS functional units. For an n-digit RNS number X = (x₁; x₂; x₃; ....; x_n) the proposed method takes at most n iterations. Each iteration requires one parallel subtractions and 2 multiplications except the first one. This scheme results in an RNS to MRC with an asymptotic complexity, in terms of arithmetic operations, in the order of O(n), while the traditional MRC technique exhibits an asymptotic complexity in the order of O (n²). In particular, the utilization of our technique, for 3-moduli and 10-moduli RNS results in the reduction of the total number of arithmetic operations required by the conversion process with 13:33% and 66:05%, respectively, when compared to state of the art MRC.