The ability to process and store information in living cells is essential for developing next-generation therapeutics and studying biology in situ. However, existing strategies have limited recording capacity and are challenging to scale. To overcome these limitations, we developed DOMINO, a robust and scalable platform for encoding logic and memory in bacterial and eukaryotic cells. Using an efficient single-nucleotide-resolution Read-Write head for DNA manipulation, DOMINO converts the living cells' DNA into an addressable, readable, and writable medium for computation and storage. DOMINO operators enable analog and digital molecular recording for long-term monitoring of signaling dynamics and cellular events. Furthermore, multiple operators can be layered and interconnected to encode order-independent, sequential, and temporal logic, allowing recording and control over the combination, order, and timing of molecular events in cells. We envision that DOMINO will lay the foundation for building robust and sophisticated computation-and-memory gene circuits for numerous biotechnological and biomedical applications.