An optical lattice is a periodic potential created by the interference of coherent light sources. Ultracold atoms can be inserted into these light crystals, which then dynamically tunnel around the structure. We demonstrate that,by tuning experimentally-accessible parameters of these systems, the transport characteristics of electronic components such as diodes and transistors can be realized. With these analogs of the fundamental building blocks of electronics, basic combinatorial logic gates, such as AND and OR gates can also be realized. These structures are interesting since their intrasystem dynamics are completely coherent. Thus, if an atom was prepared in a specific quantum state at one point in the system, that information will remain as the atom moves through the atomtronic circuit.