Several apparatuses employing a tag table and/or an AC table, and same method are provided. First, a data access apparatus, which comprises a buffer, a tag table and a controller, receives and outputs a plurality of data with at least two distinct categories in a specified sequence. The buffer stores the data of less than all the specified categories. The tag table keeps records of corresponding category information associated with the data. The data stored in the buffer is further read out under the control of the controller by referencing the corresponding category information in the tag table, so that the data access apparatus outputs the data in the specified sequence correctly. Second, an apparatus, which comprises a tag table, an AC table and a processing circuit, detects high frequency AC coefficients in a digital data processing system. The tag table includes a plurality of tag values corresponding to a plurality of DCT coefficients in an incoming DCT matrix. The AC table includes a plurality of correspondingly predetermined AC state values with at least two distinct states. The processing circuit compares the corresponding pair of the tag and AC state values to determine whether any DCT coefficient of a particular state exists in the incoming matrix.