A single chip microprocessor 1 comprises a CPU 2 and a sub-processor 5 for implementing peripheral functions of the microprocessor 1 by software. The sub-processor 5 includes electrically writable internal storage devices called a microprogram memory unit 13 and a sequence control memory unit 62 for storing the software. Peripheral functions to be implemented by the sub-processor 5 can be defined or modified by writing software into the memory units 13 and 62. Accordingly, the time it takes to define or modify the peripheral functions is the same as the time it takes to program the memory units 13 and 62. The sub-processor 5 also includes an execution unit 16 for executing a plurality of tasks and an address control circuit 14 for providing addresses to the microprogram memory unit 13 in addition to the microprogram memory unit 13 for providing microinstructions to the execution unit 16. The sequence control memory unit 62 is part of the address control circuit 14 which also includes a plurality of address registers MAR0 to MAR11. The sequence control memory unit 62 is used for storing information on what order the multiple address registers MAR0 to MAR11 are to be selected in sequentially. One of the address registers MAR0 to MAR11 is selected at every read cycle performed on the sequence control memory unit 62. A microaddress stored in the selected one of the address registers MAR0 to MAR11 is then supplied to the microprogram memory unit 13. Task null information can also be stored in the sequence control memory unit 62. The selection of one of the address registers MAR0 to MAR11 at every read cycle allows the sub-processor 5 to operate on an event driven basis.