Among a broad variety of different semiotic systems found in nature, the paradigmatic ones are the human language and the genetic code. The most striking common feature of both of these systems is the digital nature of the way information is functioning, is stored and is processed. The digital nature of the language and genetic code, I believe, were essential for the emergence of both life and human phenomena. First, the filtering mechanism provided more stability in information transmission, functioning and maintenance. An essential aspect in the emergence and evolution of these new worlds is the creation of new information.
Intonation is an example from human culture.
The question posed above, however, is whether there are any fundamental limitations for reducing all the information to the digital form. I will give examples from biology indicating that it is not possible, that the very principle of a semiotic system requires that there always be some additional information, an irreducible nondigital residue, specific for the semiotic system and essential for its being. The first example is chirality. The choice between right and left had to be done at the very beginning of life, since molecular recognition and reproduction could not be accurate enough without chiral purity. By definition, since it is a choice between two alternatives, the particular chirality of biomolecules is an information.