An integrated memory includes a circuit for testing the operation of the memory, a register circuit is used for storing a bit combination, compression unit, to receive test data which have been read from the memory cells, and a memory unit to store a plurality of bits from a compressed bit fail map. Each of the bits is associated with a different address region. One of the bits registers an error data item within the associated address region. In addition, a decoder circuit is provided for receiving the compressed address and for accessing that bit in the memory unit, which is associated with a respective address region on the basis of the compressed address. A short evaluation time for a function test on the memory and flexible alignment with the individual memory size are made possible.