Nucleic acids have been demonstrated to be versatile nanoscale engineering materials with the construction of dynamic DNA structures, motors, and circuits. These constructions generally rely on the clever use and integration of relatively few reaction mechanisms and design primitives. Here, cooperative hybridization is introduced as a mechanism in which two oligonucleotides of independent sequence can stoichiometrically, simultaneously, and cooperatively hybridize to a DNA complex. Cooperative hybridization is rigorously characterized and modeled and is shown to implement digital concentration comparison with amplification, as well as digital Boolean logic. These designs, based on cooperative hybridization, excel in being robust to impurities and not requiring oligonucleotide purification.