A display driver integrated circuit (DDI) for driving a display of image data on a display panel, an application processor (AP), a system including the DDI and the AP, and methods of operating the same are provided. The application processor includes: a controller configured to obtain a frequency of a data transmission timing control received from a display driver integrated circuit (DDI), and to generate, based on the obtained frequency, a frequency control signal for adjusting a frequency related to an operating clock signal for the DDI; a transmitter configured to transmit the generated frequency control signal to the DDI; and a frequency calculation circuit including: a detector configured to receive the data transmission timing control signal from the DDI, and a frequency calculator configured to calculate a frequency of the received data transmission timing control signal.