A power-operated toilet paper dispensing device for automatically providing a desired quantity of existing toilet paper as needed by a user may include a housing adapted to be affixed to a support surface. The novel encoder includes a first circuit for generating a fundamental sequence coded data stream from an incoming input data stream, a second circuit for generating a k-split data stream from the incoming data stream, and a third circuit for combining the fundamental sequence coded data stream and k-split data stream to form a final encoded output. For the method of the invention, the microcontroller provides a pulse-width modulation control signal to an output power stage in order to selectively control the power provided to the pump.