A graphics display system integrated circuit is used in a set-top box for controlling a television display. The graphics display system processes analog video input, digital video input, and graphics input. The system incorporates a unified memory architecture that is shared by the graphics system, a CPU, and other peripherals. The unified memory architecture uses real time scheduling to service tasks. Critical instant analysis is used to find a schedule for memory usage that does not affect memory requirements of real time tasks while at the same time servicing non-real-time tasks as needed.