every c program is converted to machine code, if this binary is distributed. Since the instruction set of a computer is well known, is it possible to get back the C original program?
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You can never get back to the exact same source since there is no meta-data about that saved with the compiled code.
But you can re-create code out from the assembly-code.
Check out this book if you are interested in these things: Reversing: Secrets of Reverse Engineering.
Edit
Some compilers-101 here, if you were to define a compiler with another word and not as technical as "compiler", what would it be?
Answer: Translator
A compiler translates the syntax / phrases you have written into another language a C compiler translates to Assembly or even Machine-code. C# Code is translated to IL and so forth.
The executable you have is just a translation of your original text / syntax and if you want to "reverse it" hence "translate it back" you will most likely not get the same structure as you had at the start.
A more real life example would be if you Translate from English to German and the from German back to English, the sentance structure will most likely be different, other words might be used but the meaning, the context, will most likely not have changed.
The same goes for a compiler / translator if you go from C to ASM, the logic is the same, it's just a different way of reading it ( and of course its optimized ).
I would guestimate the conversion rate of a really skilled hacker at about 1 kilobyte of machine code per day. At common Western salaries, that puts the price of, say, a 100 KB executable at about $25,000. After spending that much money, all that's gained is a chunk of C code that does exactly what yours does, minus the benefit of comments and whatnot. It is no way competitive with your version, you'll be able to deliver updates and improvements much quicker. Reverse engineering those updates is a non trivial effort as well.
If that price tag doesn't impress you, you can arbitrarily raise the conversion cost by adding more code. Just keep in mind that skilled hackers that can tackle large programs like this have something much better to do. They write their own code.
One of the best works on this topic that I know about is:
Pigs from sausages? Reengineering from assembler to C via FermaT.
The claim is you get back a reasonable C program, even if the original asm code was not written in C! Lots of caveats apply.
It depends on what you mean by original C program. Things like local variable names, comments, etc... are not included in the binary, so there's no way to get the exact same source code as the one used to produce the binary. Tools such as IDA Pro might help you disassemble a binary.
You can try hex-rays.com, it has a really nice decompiler which can decompile assembly code into C with 99% accuracy.
The Hex-Rays decompiler (extension to IDA Pro) can do exactly that. It's still fairly recent and upcoming but showing great promise. It takes a little getting used to but can potentially speed up the reversing process. It's not a "silver bullet" - no c decompiler is, but it's a great asset.