Magnetic domain walls (MDWs) can move when driven by an applied magnetic field. This motion is important for numerous devices, including magnetic recording read/write heads, transformers and magnetic sensors. A magnetic film, with a sawtooth profile, localizes MDWs in discrete positions at the narrowest parts of the film. We propose a controllable way to move these domain walls between these discrete locations by applying magnetic field pulses. In our proposal, each applied magnetic pulse can produce an increment or step-motion for an MDW. This could be used as a shift register. A similarly patterned magnetic film attached to a large magnetic element at one end of the film operates as an XOR logic gate. The asymmetric sawtooth profile can be used as a ratchet resulting in either oscillating or running MDW motion, when driven by an ac magnetic field. Near a threshold drive (bistable point) separating these two dynamical regimes (oscillating and running MDW), a weak signal encoded in very weak oscillations of the external magnetic field drastically changes the velocity spectrum, greatly amplifying the mixing harmonics. This effect can be used either to amplify or shift the frequency of a weak signal. Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/49053/2/njp5_1_082.pdf