This paper presents a novel adaptable 4-moduli set {2n + k, 2n+1, 2n-1, 22n+1}. It offers diverse dynamic ranges (DRs) from 25n-2n to 25n + k-2n + k that are used to conquer the over-range issue in RNS-application hardware designs. The proposed adaptable set possesses the coarse parameter n and fine parameter k. It not only has better parallelism and larger dynamic range (DR) than the existing adaptive 3-moduli sets, but also holds more sizable and flexible than the general 4-moduli sets with single parameter. For the adaptable R-to-B conversion, this paper first derives a fast reverse converting algorithm based on Chinese Remainder Theorem (CRT) and then presents the efficient converter architecture. From the experimental results, the proposed adaptable converter achieves better hardware performance in various DRs. Based on TSMC 0.18 µm CMOS technology, the proposed converter design is implemented and its results get at least 20.93% saving of Area-Delay-Power (ADP) products on average when comparing with the latest converter works.