In this paper, residue to binary conversion is presented for the four moduli setsharing a common factor. A new and efficient converter for the moduli set using multipliers, carry saves and modular adders is proposed based on a cyclic jump approach. A theoretical hardware implementation and comparison with a state-of- the- art scheme showed that the proposed scheme performed better. The 4- moduli set selected provides a larger dynamic range which is needed for Digital Signal Processing (DSP) applications [7].