PURPOSE: To shorten a processing time and to execute rapid coordinate conversion by computing only parallel movement elements for coordinate conversion at the time of moving parallel.

CONSTITUTION: The coordinate conversion system is provided with a matrix computing part for computing only the parallel movement elements of a coordi nate matrix, whether parallel movement or not is judged based upon the contents of a command for commanding coordinate conversion matrix operation, and at the time of moving in parallel, only the parallel movement elements in the coordinate matrix are computed by a matrix computing part. Namely, a classifying parameter included in the 2nd element set up in the command indicating parallel movement e.g. or not and shown in the command formats is identified without always computing all the elements in the applied matrix to omit a part of processing for parallel movement. Thus, the coordinate conver sion can rapidly be processed.