a scanning format conversion circuit for performing the mutual conversion between a progressive scanning format and a zig - zag scanning format to read or write n × n discrete cosine transform coefficients from or into a memory in a coding process or a decoding process of a video system . the scanning format conversion circuit comprises a pure logic circuit including an up / down counting circuit , a down counting circuit , first to third selection circuits , a comparison circuit , a phase change circuit , and an accumulation circuit . with this construction , the mutual conversion between the progressive scanning format and the zig - zag scanning format is performed on the basis of the rule between the input orders and the actual positions of the discrete cosine transform coefficients . therefore , the scanning format conversion circuit is capable of simplifying the implementation of asic and performing the scanning format conversion operation regardless of a block size .