The duotronic computer system was designed by Doctor Richard Daystrom in 2243. It was used aboard Constitution-class starships in the mid-23rd century, including the USS Enterprise. Daystrom's achievements with this system ultimately earned him the Nobel and Zee-Magnees Prizes. (TOS: "The Ultimate Computer")
In 2268, Daystrom developed a new multitronic system which was to supersede the older duotronic system. However, tests for the new M-5 computer failed and the duotronic system remained. (ENT: "The Ultimate Computer")
Among the systems using duotronic technology aboard Enterprise was its sensor array. (DS9: "Trials and Tribble-ations") The duotronic system was ultimately replaced by isolinear circuitry in the 24th century. (TNG: "Relics")