We present a scheme for a molecular memory, which is based on the influence of the positions of chemical side-groups attached to aromatic molecules on the paths for electrons propagating through these molecules in the ballistic and tunnelling transport regimes. Using the elastic scattering quantum chemistry technique in a topological Hückel implementation, we show how it is possible to represent four different output states with a benzene molecule attached to one input and three output electrodes. To achieve this we choose single atomic orbitals as side-groups and by varying their number and positions the desired output pattern is met, at least in the ballistic regime. This case is also compared to the situation where only two electrodes are attached; the differences with respect to the tunnelling regime are analysed in detail. Since our scheme is based on path and therefore phase differences in electronic wave propagation, we also compare its properties with those of other interference-based concepts for information processing, such as quantum computing or photonics.