 Since the information in the building blocks, 100, 10 and 1, is given the number representation can still be reconstructed. This implies that natural numbers code in terms of addition of powers of  k in principle two types of information: value and frequency. We can use this insight to code complex typed information in single natural numbers. Basically it allows us to code any natural numbers in a string of symbols of length \(\lceil \log_k n \rceil \), which specifies a quantitative measure for the amount of information in a number in terms of the length of its code. See  section 3.3  for a historical analysis of the importance of the discovery of position systems for information theory. 