I have two threads in my application. Is it possible to execute both the threads simultaneously without sleeping any thread?
Yes, if you have multiple processors or multi-core processors. One thread will run in one core.
C does not, itself, have any means to do multi-threaded code.
However, POSIX has libraries that allow you to work with threads in C.
One good article about this topic is How to write multi-threaded software in C and C++.
You can run the threads parallel in your application especially if they are not waiting on each other for some inputs or conditions. For example: One thread may be parsing a file and other maybe playing a song in your application.
Generally OS takes care of the thread time slicing. So at the application level it would look like these threads are running parallel but the OS does the time slicing giving each thread certain execution time.
With multi-core processors/cores it is possible to run the threads parallel in realtime, however the OS decides which threads to run unless you specifically code at lower level to ensure which threads you want to run in parallel.
As others have mentioned, with multiple cores it is possible, but, it depends on how the OS decides to distribute the threads. You don't have any control, that I have seen, on dictating where each thread is ran.
For a really good tutorial, with some nice explanation and pictures you can look at this page, with code as to how to do multi-threading using the POSIX library.
http://www.pathcom.com/~vadco/parallel.html
The time slice for sleep is hard to see, so your best bet is to test it out, for example, have your two threads begin to count every millisecond, and see if the two are identical. If they are not, then at least one is going to sleep by the cpu.
Most likely both will go to sleep at some time, the test is to see how much of a difference there is between the two threads.
Once one thread blocks, either waiting to send data, or waiting to receive, it will be put to sleep so that other threads can run, so that the OS can continue to make certain everything is working properly.