A semiconductor memory has a field programmable unit in which logic to inter-convert external signals to be input/output to/from a memory system and internal signals to be input/output to/from a memory cell array is programmed. A program for constructing the logic of the field programmable unit is stored in a nonvolatile program memory unit. Through the field programmable unit, a controller can access the memory cell array, even when the interface of the controller accessing the semiconductor memory is different from an interface for accessing the memory cell array. Therefore, one kind of semiconductor memory can be used as plural kinds of semiconductor memories. This eliminates the need to develop plural kinds of semiconductor memories, reducing a development cost.