This paper presents a residue number system to binary converter in the four moduli set {2n - 1, 2n, 2n + 1, 2n + 1 - 1}, valid for even values of n. This moduli set is an extension of the popular set {2n - 1, 2n + 1}. The number theoretic properties of the moduli set of the form 2n ± 1 are exploited to design the converter. The main challenge of dealing with fractions in Residue Number System is overcome by using the fraction compensation technique. A hardware implementation using only adders is also proposed. When compared to the common three moduli reverse converters, this four moduli converter offers a larger dynamic range and higher parallelism, which makes it useful for high performance computing.