A magnetic shift register utilizes a data column comprising a thin wire of magnetic material. A writing element selectively changes the direction of the magnetic moment in the magnetic domains to write the data to the data column. Associated with each domain wall are large magnetic fringing fields concentrated in a very small space. These magnetic fringing fields write to and read from the magnetic shift register. When the domain wall is moved close to another magnetic material, the fringing fields change the direction of the magnetic moment in the magnetic material, effectively "writing" to the magnetic material. A reading element similar to a tunneling junction comprises a free layer and a pinned layer of magnetic material. Fringing fields change the direction of the magnetic moment in the free layer with respect to the pinned layer, changing electrical resistance of the reading element and "reading" data stored in the magnetic shift register.