(Disclaimer: I am not a biologist) DNA can only have four bases (ACGT), so each DNA base can only encode 2 bits of information. 20 amino acids could be encoded

(Disclaimer: I am not a biologist) DNA can only have four bases (ACGT), so each DNA base can only encode 2 bits of information. 20 amino acids could be encoded in 4 and a bit bits, not 20 bits (actually, you need a stop code, so 21 codes are needed). As it is, DNA uses 3 bases, 6 bits to encode each amino acid, so there is a little redundancy. See http://en.wikipedia.org/wiki/Genetic_code#RNA_codon_table http://en.wikipedia.org/wiki/Genetic_code#RNA_codon_table for the mapping. Proteins are 3D entities, but their shape is determined by the amino acids, which are determined by the DNA - so there is no awesome compression here. To put it another way, the words "booktitle:Dune" encode a novel, which is much more than 14 bytes, but I cannot encode any arbitrary stream of bytes in this way.