An address generator is provided for generating addresses for testing an addressable circuit. The address generator can include a base address register for buffer-storing a base address. The base address register can be assigned an associated offset register group having a plurality of offset registers for buffer-storing relative address values. Further, the address generator can include a first multiplexer circuit which is dependent on a base register selection control signal, switches through an address buffer-stored in the base address register to a first input of an addition circuit and to an address bus, which is connected to the circuit to be tested. A second multiplexer circuit can be dependent on the base register selection control signal, through-connects the offset register group associated with the through-connected base address register to a third multiplexer circuit, which is dependent on an offset register selection control signal.