Decimal counter ($A\in \{0,\dots ,9{\}}^k$)

A decimal counter stores a nonnegative integer using an array of base-ten digits, with the least significant digit first. Increment resets trailing nines and increases the next digit, or wraps modulo $10^k$ if all $k$ digits are nines. Starting at zero, the exact number of digit changes in $n$ increments is ${\sum }_{i=0}^{k-1}\lfloor n/10^i\rfloor \le 10n/9$. This is an aggregate analysis proving a constant amortized cost per increment under unit-cost digit updates. An arbitrary initial value contributes an additional $O(k)$ in Big O notation.