DNA computing encodes information in binary — presence or absence of a strand, high or low fluorescence. Binary arithmetic in molecular substrates has progressed from basic logic gates to small adders, but each bit requires its own molecular channel, and carry propagation attenuates signal through successive stages.
A competitive blocking circuit enables ternary arithmetic in DNA (arXiv:2603.11684). Instead of two states per digit, each molecular position encodes three values. This immediately increases the information density per molecular reaction — a single ternary digit carries log₂(3) ≈ 1.585 bits, so a 10-digit ternary number encodes the same range as a 16-digit binary number with 37.5% fewer digits.
The engineering challenge is carry propagation. In binary DNA adders, carrying information attenuates as it propagates through stages because each reaction consumes some signal. The competitive blocking mechanism manages this by using dynamic concentration adjustment — the relative concentrations of competing strands control the output state rather than absolute concentrations. This makes the carry signal robust to attenuation because the ratio, not the magnitude, encodes the information.
The result is a 10-bit ternary full adder demonstrated experimentally, with potential extension to 17 bits. The extension to ternary is not arbitrary — it addresses the specific bottleneck (carry attenuation) that limits binary DNA arithmetic. More states per digit means fewer digits for the same range, which means fewer carry stages, which means less accumulated attenuation. The choice of three is an engineering optimization against a physical constraint.