A generalization of a new generic 4-modulus base for residue number systems (RNS) is presented in this paper. An efficient RNS to binary conversion algorithm and a hierarchical architecture for these bases are also described. The key features of our conversion architecture compared to previous published architectures of the same output range are a larger moduli set selection and savings on the critical delay, area and power. The FPGA implementation and the detailed proof supporting it are also discussed.