Cracking the code of life marked an interesting and significant beginning of life science. The genetic code maps the 20 amino acids to all 64 possible arrangements of the four (4) nitrogenous bases. Since its deciphering, various designs in varied fields have been proposed. This work presents a Residue Number System (RNS)-based genetic code using the concept of number tree. In conformity with Gamow’s postulation, (43 = 4 × 4 × 4 = 64) we present a three moduli set RNS model of the genetic code. The design sorts the codes into their “family box” or “four-codon box”. The application of RNS in bioinformatics is not new - notably its application to Smith-Waterman Algorithm. The capability of RNS to generate the genetic code is novel and significantly draws a convergence point between the mathematics of number systems, thus RNS, and the foundations of molecular biology, the genetic code.