We investigated several classes of two coupled Aharonov-Bohm rings that share a finite center common path, where the phase of the electron wave function can be modulated by two distinct magnetic fluxes. The coupling is similar to two coupled atoms. The behavior of charge accumulation along the center common path or, equivalently, the bonding and anti-bonding of the two rings can be achieved as the two applied fluxes are varied. Thus, when three external terminals are connected to such coupled rings, the behavior of the electron transport is divided into several classes, depending on the number of atoms in each ring and the locations of the terminals. The results are presented here. The applicable electron wave computing circuits are discussed. In particular, a half-adder construction is shown here by employing the symmetric and anti-symmetric properties of the transmission of a given terminal when the sign of the flux is changed. The analogy of two coupled rings with respect to two spins allows one to make a further connection with traditional spintronics-based schemes.