A system for decompressing a bit stream of compressed data representing a plurality of image blocks. This includes a two-step method of processing both a DC code and a plurality of AC codes. With respect to the processing of the AC codes, a plurality of bits of compressed input data relating to the AC codes are first retrieved from the bit stream. A first decoding operation is then executed based on the obtained compressed input data in order to generate first output data. It is then determined whether sufficient space is available for the first output data. If it is determined that there is sufficient space for the first output data, the first output data is outputted. On the other hand, if it is determined that there is insufficient space for the first output data, an alternate second decoding operation is executed in order to generate second output data.