A data processing system includes a buffer, a design under checking (DUC), and a self-checking circuit. The buffer is used to buffer data generated from a source device. The DUC is used to perform a designated function upon data read from the buffer when operating under a normal mode. The self-checking circuit is used to apply logic functional checking to the DUC when the DUC operates under a self-checking mode. When the DUC operates under the self-checking mode, the buffer keeps buffering data generated from the source device.