Electron transmission characteristics through a generalized three-terminal clean Aharonov-Bohm ring is investigated with an arbitrary terminal configuration. This three-terminal ring is shown to be the most basic quantum resistor network that is suitable for electron wave computing, as we demonstrate in this work. There are four basic classes of three-terminal rings. The scaling relation in each class is deduced. Thus the transmission characteristics in each class are valid from an atomic-scale-sized ring to a mesoscopic-scale-sized one, limited only by the electron phase-breaking length. The Buttiker symmetry rule is essential when searching for basic logic functions. Logic functions such as IF-THEN, AND, OR, XOR, and INVERT are shown here as the basic building blocks for a possible massive parallel electron wave computing machine. The node equation method, linking the wave function of one terminal node with its neighboring terminal nodes, is used. The rules governing each terminal node are summarized. This method is equivalent to the Kirchhoff current conservation law in classical circuit theory.