A digital memory based on a memory cell having two magnetoresistive, ferromagnetic film portions separated by an intermediate layer, all of limited thickness. Each of the magnetoresistive film portions is less than 300 .ANG. thick and the intermediate layer is less than 100 .ANG. thick. Conductive wordlines separated from the upper magnetoresistive film by an insulating layer are utilized, in conjunction with sense current which passes through the cells, to select particular cells for read or write operations.