For each genetic codon, which is composed of 3 base pairs, the amount of information is I=H unknown -H known =3 log 2 (4)-0 = 6 bits. For each amino acid, because many amino acids have more than one codon, the information content is different. For example, proline has 4 codons and the third base pair of the codons is wobbled, the information content of proline C=H max -H known =6-2 = 4 bits. In the same way, the information content of Arg is 3 bits, of Asn is 5 bits, and of Trp is 6 bits. Organisms probably know the importance of each amino acid and how to regulate gene expressions with codon bias, and evolved this codon system to regulate translation efficiently and reduce the harm of mutation of important amino acids. The redundance of information is R=I-C. The less the information content is, the more the redundance of information, the more the space to silence or neutralize mutation. So Arg is more important, more protected from mutation, and more expression regulated than Trp. Although some amino acids may need less information to be encoded (for example, 2 base pairs for the amino acids with information content less than 4 bits), organisms actually use 3 base pairs for every amino acid, so it cost organisms 6 bits genomic information to encode every amino acid. In another word, the amount of information of every amino acid in genome is 6 bits although there is information redundance in the 6 bits.