Real Time System

The commonly accepted definition of "real-time" performance is that real-world events must be responded to within a defined, predicable, and relatively short time interval.
When the correctness of the computations not only depends upon the logical correctness but also upon the time at witch the result is produced (the system fails If the timing constraints are not met) To guarantee the timing behavior requires that the system be predictable.

Real Time Operating System

The principal responsibility of a real-time (RT) operating system (RTOS) can be summarized as that of producing correct results while meeting predefined deadlines in doing so.
Therefore, the computational correctness of the system depends on both the logical correctness of the results it produces, and then timing correctness, i.e. the ability to meet deadlines, of its computation

It is a priority-based pre-emptive multitasking kernel which supports the essential functions of task, semaphore, queue, and memory management. The core is written in C, but there are a few target dependent callback functions required to handle task initialization and task switching. The basic role of RTOS is same as general OS, but it must perform a task in a given time period. Failure to meet the time deadline will have consequence of varying severity.

Generally, RTOS is used to Embedded System,. However, all OS of Embedded System are not RTOS because all embedded system need exact time. For example, in a recharger system, time is no so critical problem.