DNA logic circuits are based on DNA molecular programming that implements specific algorithms using dynamic reaction networks. Particularly, DNA adder circuits are key building blocks for performing digital computation. Nevertheless, existing circuit architectures are limited by scalability for implementing multi-bit adder due to the number of required gates and strands. Here, we develop a compact-yet-efficient architecture using cooperative strand displacement reactions (cSDRs) to construct DNA full adder. By exploiting a parity-check algorithm, double-logic XOR-AND gates are constructed with a single set of double-stranded molecule. One-bit full adder is implemented with three gates containing 13 strands, with up to 90% reduction in strand complexity compared to conventional circuit designs. Using this architecture and a transmitter on magnetic beads, we demonstrate DNA implementation of 6-bit adder on a scale comparable to that of a classic electronic full adder chip, providing the potential for application-specific circuit customization for scalable digital computing with minimal reactions.