The analysis of proteins at the single-molecule level uncovers heterogeneous behaviors that are masked in ensemble-averaged techniques. The digital quantification of enzymes traditionally involves the observation and counting of single molecules partitioned into microcompartments via the conversion of a pro-fluorescent substrate. This strategy based on linear signal amplification is limited to a few enzymes with sufficiently high turnover rate. Here we show that by combining the sensitivity of an exponential molecular amplifier with the modularity of DNA-enzyme circuits and droplet readout allows to specifically detect, at the single-molecule level, virtually any D(R)NA-related enzymatic activity. This strategy, denoted digital PUMA, is validated for more than a dozen different enzymes, including many with slow catalytic rate, and down to the extreme limit of apparent single turnover for S. pyogenes Cas9. Digital counting uniquely yields absolute molar quantification and reveals a large fraction of inactive catalysts in all tested commercial preparations. By monitoring the amplification reaction from single enzyme molecules in real-time, we also extract the distribution of activity among the catalyst population, revealing alternative inactivation pathways under various stresses. Our approach dramatically expands the number of enzymes that can benefit from quantification and functional analysis at single-molecule resolution. We anticipate digital PUMA to serve as a versatile framework for accurate enzyme quantification in diagnosis or biotechnological applications. These digital assays may also be utilized to study the origin of protein functional heterogeneity.