Random numbers can be generated in a statistically independent manner and with identical probability if the bits generated by a controlled bit generator are stored by a storage in a plurality of memory regions, wherein the bits are each stored in such memory regions associated with a difference of the bits of the values 1 and 0 generated up to the time of storage, and if all the bits stored within a memory region are subjected to algorithmic post-processing as soon as a predetermined number of bits within a memory region is exceeded. The fact that the bits are not stored and processed sequentially, i.e. in the order of generation, allows using a sequence of bits within which the individual bits are statistically independent of one another for the algorithmic post-processing. Thus, a way of performing algorithmic post-processing of the bits without reducing the entropy is provided.