Here's an interesting comment from Ian Grigg on how fungibility requirements impact representation in the digital realm:
Bank notes: payment systems (which is the general class in which bank notes fall) desire a thing called fungibility – the ability for one note of $10 to be equivalent to another. This is far more important than issues such as traceability or privacy.
Because of this, the tendency in the digital world is to use straightforward accounting systems that simply count up the numbers and allocate them in accounts. If we are digital, we don't need to use the clumsy token method, as that is more work for little gain. We simply say “pass 10 from Alice to Bob.” Obviously, we may want to wrap that up in strong crypto, and we may want to worry about privacy, etc, if that's what is called for. But these are separate, derivative issues.
One big question however is (as intimated) what the note or accounts represent. The set of claims that makes up a note is varied and complex. Skipping forward, what these claims reduce to is a contract between the issuer and the holder. And, it so happens we have an easy way to issue digital contracts and even identify them: the issuer writes a document, signs it digitally, and hashes it. The hash becomes the identifier, and thereonafter, the accounts are in that hash.
This works as well for token money like eCash coins. For more info on this, see the Ricardian Contract.