Alice and Bob should be able to approach a provider or exchange house and request digital cash breakdowns into the smallest possible units. Or Alice should be able to sign some sort of check and fill in the amount of money that she wants to pay to Bob. In the first approach, a digital cash token in a given amount can be subdivided into smaller pieces of cash in smaller amounts. The cash must be fungible so that a reasonable portions of change can be made. The smaller the better to enable high quantities of small-value transactions.
The second approach would require special encryption techniques to allow filling in the amount of money that you want to pay onto some sort of digital check. A check would be certified from the bank up to a certain value. This kind of approach could not be anonymous, for the bank must know who issued the check in order to debit the amount of money that he has spent from his account.