From a mathematical point of view, the genetic code is a surjective mapping between the set of the 64 possible three-base codons and the set of 21 elements composed of the 20 amino acids plus the Stop signal. Redundancy and degeneracy therefore follow. In analogy with the genetic code, non-power integer-number representations are also surjective mappings between sets of different cardinality and, as such, also redundant. However, none of the nonpower arithmetics studied so far nor other alternative redundant representations are able to match the actual degeneracy of the genetic code. In this paper we develop a slightly more general framework that leads to the following surprising results: i) the degeneracy of the genetic code is mathematically described, ii) a new symmetry is uncovered within this degeneracy, iii) by assigning a binary string to each of the codons, their classification into definite parity …