The computer technology invented by Dr Richard Daystrom that formed the basis of Starfleet computer systems in the 23rd century, including those of the original USS Enterprise.
Duotronics was the breakthrough that made Richard Daystrom famous. He devised it while still in his twenties and it won him the Nobel and Zee-Magnees prizes. Duotronic systems run the computers of Constitution-class starships during Kirk's five-year mission.
The technology is discussed in the Original Series episode The Ultimate Computer, set in 2268. Daystrom, struggling to equal his early success, installs the M-5 multitronic unit aboard the Enterprise as duotronics' intended successor. The M-5, patterned on his own unstable mind, attacks other starships during war games and has to be shut down.
Duotronics therefore stayed in service for decades more. In The Next Generation episode Relics, Scotty is at home with the duotronic systems of the old USS Jenolan. By then Starfleet has moved on to isolinear technology.