1. A multiplexer/de-multiplexer memristive device comprising: a memristive matrix, said memristive matrix containing mobile dopants; programming electrodes, said programming electrodes being configured to apply an electrical field across said memristive matrix such that said mobile dopants form a conductive band, said conductive band remaining stable after removal of said electrical field; a base electrode, said base electrode being disposed along a first side of said memristive matrix; and a plurality of input/output electrodes disposed on a second side of said memristive matrix, said programming electrodes selectively applying said electrical field such that said conductive band selectively forms an electrical connection between said base electrode and one of said plurality of input/output electrodes.