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The magnetic hysteresis of a film consisting of a single magnetic domain is analyzed. A method of designing logical computer elements employing thin films is presented and illustrated. It is concluded that recently discovered films approaching single domain behavior offer two possible advantages in applications: 1) As a storage element in a memory array a film can be switched faster than presently available polycrystalline cores. 2) A film can be used to perform a variety of logical operations more simply, in principle, than it is possible with polycrystalline cores.