revolution,

NULL is (as of C1X April 2011 draft) an implementation-defined null pointer constant. OTOH, chapter "6.3.2.3 Pointers" clause 3 says that "An integer constant expression with the value 0, or such an expression cast to type void *, is called a null pointer constant."

There are some other references to void * type. For example, chapter "6.2.5 Types" clause 28 tells that "A pointer to void shall have the same representation and alignment requirements as a pointer to a character type."

Caveat emptor.

That sounds more like the reality. I couldn't see any reason why NULL has to be always zero. It is only by convention that people expect it to be zero. And I think that to be a genuine NULL it should exist outside of the number space completely and not have any numeric value. Indeed.

What would its value be then?

If you are asking how would it be represented then that would be implementation defined. A possible method is to associate an extra bit with each pointer that indicates whether it is null or not.