An apparatus that contains an instruction processing circuit (14), a main memory (18) addressable by the instruction processing circuit (14) and a cache memory (16). In a normal mode the cache memory (16) is used to cache a part of data and/or instructions that the instruction processing circuit (14) addresses in the main memory (18) during execution, and to substitute cached data and/or instructions when the instruction processing circuit (14) addresses the data and/or instructions in the main memory (18). The circuit is able to switch to a low power operating mode. Upon the switch an interrupt program for executing a function during operation in the low power operating mode is loaded into the cache memory (16) from the main memory (18). Power supply to the main memory (18) is then switched off, but keeping at least a part of the cache memory (16) continuous to receive power supply. This part ensures that the program of instructions for executing the function is available to the instruction processing circuit. The program is executed from said at least part of the cache memory (16) in the low power operating mode.