This paper presents a new residue number system (RNS) to binary converter for the novel four-moduli set {2^n/2 -1, 2^n/2 +1, 2ⁿ +1, 2²ⁿ⁺¹ -1} for even n, based on new Chinese remainder theorem 1 (New CRT-I). Due to the simple multiplicative inverses of the proposed moduli set, it can considerably reduce the complexity of the RNS to binary converter. The presented converter architecture is adder-based, and it has better performance in terms of hardware requirements and conversion delay than the latest designs of the RNS to binary converters for another 4-moduli set with the same dynamic range.