DNA circuits form the basis of programmable molecular systems capable of signal transduction and algorithmic computation. Some classes of molecular programs, such as catalyzed hairpin assembly, enable isothermal, enzyme-free signal amplification. However, current detection limits in DNA amplification circuits are modest, as sensitivity is inhibited by signal leakage resulting from noncatalyzed background reactions inherent to the noncovalent system. Here, we overcome this challenge by optimizing a catalyzed hairpin assembly for single-molecule sensing in a digital droplet assay. Furthermore, we demonstrate digital reporting of DNA computation at the single-molecule level by employing ddCHA as a signal transducer for simple DNA logic gates. By facilitating signal transduction of molecular computation at pM concentration, our approach can improve processing density by a factor of 104 relative to conventional DNA logic gates. More broadly, we believe that digital molecular computing will broaden the scope and efficacy of isothermal amplification circuits within DNA computing, biosensing, and signal amplification in general.