Embodiments of the invention provide a multi-terminal resistance device with first and second electrodes, a shared third electrode, and a resistance layer providing first and second current paths between the shared third electrode and the first and second electrodes, respectively. A current state of the device may be programmed by applying one or more electrical signals along the first and/or second current paths to change a resistance of the device. In some embodiments, applying an electrical signal may switch a junction resistance of the first and/or second electrodes and the resistance layer between two or more resistance values. The device may include a shared fourth electrode to provide extra programming capability. In some embodiments, the device may be used to store a data state, to determine a count of multiple electrical signals, or to perform a logic operation between two electrical signals.