1. A multiplexer/de-multiplexer memristive device ( 300 ) comprising: a memristive matrix ( 370 ), said memristive matrix ( 370 ) containing mobile dopants; programming electrodes ( 310 , 320 ), said programming electrodes ( 310 , 320 ) being configured to apply an electrical field across said memristive matrix ( 370 ) such that said mobile dopants form a conductive band ( 380 ), said conductive band ( 380 ) remaining stable after removal of said electrical field; a base electrode ( 330 ), said base electrode ( 330 ) being disposed along a first side of said memristive matrix ( 370 ); and a plurality of input/output electrodes ( 340 , 350 , 360 ) disposed on a second side of said memristive matrix ( 370 ), said programming electrodes ( 310 , 320 ) selectively applying said electrical field such that said conductive band ( 380 ) selectively forms an electrical connection between said base electrode ( 330 ) and one of said plurality of input/output electrodes ( 340 , 350 , 360 ).