A multi-stage algorithmic pattern generator, which generates bit streams for testing IC chips, is comprised of an initial stage, an intermediate stage, and an output stage which are coupled together as a three stage pipeline. The initial stage sequentially generates multiple sets of virtual addresses for a virtual memory in response to a series of instructions from an external source. The intermediate stage sequentially stores each set of virtual addresses from the initial stage and translates the stored set of virtual addresses into a set of physical addresses for an actual memory that is to be tested. The output stage sequentially stores each set of physical addresses form the intermediate stage and generates output signals for testing the memory chips, by selecting bits from the stored set of physical addresses.