Entropy of sums of random digits

Abstract The amount of information conveyed by check sums in digital sequences is conveniently measured by entropy. We determine the entropy of sums of binary digits and, more generally, r+1 digits 0,…,r for r⩾1. For finite sequences of independent identically distributed binary digits this is the entropy of a binomial distribution. We generalize to Poisson distributions and to Markovian sequences of binary digits. We also consider approximations and upper and lower bounds to the entropies.