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A photoelectronic circuit consists of a combination of electroluminescent cells and photoconductors, interconnected by electrical as well as optical paths. A study is made of the properties of electroluminescent cells and photoconductors, and of the applications of these elements to the design of switching circuits. The asymmetrical bistable stage is taken up in detail, and analyzed with a view to determining its advantages and disadvantages. It is shown that this stage suffers from the inherent disadvantage that any improvement in the speed of turn-on results in a deterioration of the recovery characteristic. Furthermore, the switching requirements for turn-on and turn-off are dissimilar. A symmetrical version of this circuit is also presented; this circuit eliminates many of the disadvantages of the asymmetrical version, and also considerably speeds up the recovery characteristic without increasing the turn-on time. Circuits are developed for performing the logical operations of transmission, negation, conjunction and disjunction, and their principles of operation are described. In conclusion, techniques are developed for the synthesis of over-all computing operations, such as those of a half-adder, even parity checker, and a shift register.