I was thinking to senario like this:
I will create a text area where I will allow student to write their C code in that text area.
I wanna create a button called [Compile].
This button will compile my C code in text area.
(Expectation: The compile button will compile my C code and give the output exactly the same as gcc compiler)
Could someone let me know how to start with it.

It's possible to use the exec,passthru and system functions to call external programs from a PHP script and return their output. Exec returns the output to an array rather than outputting raw data, so this may be more suitable.

The steps I would take to approach this:
1) Fetch code from textarea and write to a new C source file.
2) Use exec to pass the file to your compiler and return the output.
3) Output the array.

There may be a more elegant means of dealing with external programs but this is the best method that springs to mind.