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Why are codons made of three RNA bases?

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Diagram of a DNA polynucleotide chain showing linked deoxyribose sugars, phosphate groups, and nitrogenous bases (adenine, guanine, cytosine, thymine), with an inset comparing ribose and uracil in RNA. — Nucleic acid A portion of the polynucleotide chain of deoxyribonucleic acid (DNA), with an inset showing the corresponding pentose sugar and pyrimidine base in ribonucleic acid (RNA).

Codons are composed of three RNA bases because this triplet structure provides enough combinations to encode the 20 amino acids required for protein synthesis.12

Because there are four different nitrogenous bases available (adenine, guanine, cytosine, and uracil), a sequence of three nucleotides allows for $4^{3}$ , or 64, possible unique combinations. This is essential because:2

Encoding Amino Acids: Of these 64 possible codons, 61 specify the 20 amino acids used to build proteins.13
Degeneracy: Since there are more codons than amino acids, most amino acids are specified by more than one codon, a feature known as the degeneracy of the genetic code.14
Termination: The remaining three codons (UAG, UAA, and UGA) serve as stop signals to terminate the process of translation.12

The structure of the genetic code, where many amino acids are determined by the first two bases of the codon, suggests that it may have evolved from a more primitive system that utilized 16 dinucleotides.4