Halftone generating methods and systems convert continuous tone anti-aliased image data to halftone image data using halftoning techniques that efficiently use memory resources. One of a plurality of Holladay counters is selected and the address bits from the selected Holladay counter are output to a look-up table that efficiently stores various halftone screens. Halftone image data is then output. If necessary, the halftone image data is unpacked and replicated as required depending on the resolution requirements of the halftone screen.