DNA is a compelling alternative to non-volatile information storage technologies due to its information density, stability, and energy efficiency. Previous studies have used artificially synthesized DNA to store data and automated next-generation sequencing to read it back. Here, we report digital Nucleic Acid Memory (dNAM) for applications that require a limited amount of data to have high information density, redundancy, and copy number. In dNAM, data is encoded by selecting combinations of single-stranded DNA with (1) or without (0) docking-site domains. When self-assembled with scaffold DNA, staple strands form DNA origami breadboards. Information encoded into the breadboards is read by monitoring the binding of fluorescent imager probes using DNA-PAINT super-resolution microscopy. To enhance data retention, a multi-layer error correction scheme that combines fountain and bi-level parity codes is used. As a prototype, fifteen origami encoded with 'Data is in our DNA!\n' are analyzed. Each origami encodes unique data-droplet, index, orientation, and error-correction information. The error-correction algorithms fully recover the message when individual docking sites, or entire origami, are missing. Unlike other approaches to DNA-based data storage, reading dNAM does not require sequencing. As such, it offers an additional path to explore the advantages and disadvantages of DNA as an emerging memory material.