  Many digital functions studied in the literature, e.g., the summatory
function of the base-$k$ sum-of-digits function, have a behavior showing some
periodic fluctuation. Such functions are usually studied using techniques from
analytic number theory or linear algebra. In this paper we develop a method
based on exotic numeration systems and we apply it on two examples motivated by
the study of generalized Pascal triangles and binomial coefficients of words.
