This question is kind of long-detailed and took a lot of my time; hope you read it till end; thanks for your patience

I've find out that size of data in some programming languages like python isn't really matter, and they can store very big values like huge numbers; and then increase them to something even bigger.
I work with c and I know in that language, variables must have a particular type and size. To store huge integers (which is very bigger than the largest type in c), I know 2 different ways:

First method: Using char pointer and store each digit at particular index

• First value of pointer can tell us the sign.
• Pointer can stop at particular value (like \0 in strings but now we use $).

to store 123456789 pointer would be like this:

++++++++++++++++++++++++++++++++++++++++++++ | + | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9| $ | ++++++++++++++++++++++++++++++++++++++++++++ ^ ^ | | sign finisher 

Second method: Using unsigned int pointer and store numbers like computers store binaries (I mean store them based on size of int)

• First value of pointer can tell us the sign
• Second value of pointer can tell us the length

to store 123456789 pointer would be like this:

// 123456789 MOD 2^32 = 123456789 +++++++++++++++++++++++++++++++++++ | + | 1 |123456789| +++++++++++++++++++++++++++++++++++ ^ ^ ^ | | | sign length value 

and to store something bigger like 9998877665544332211 the pointer would be as in below:

// 9998877665544332211 / 2^32 = 2328045122 // 9998877665544332211 MOD 2^32 = 2942002099 +++++++++++++++++++++++++++++++++++++++++++++++ | + | 1 |2942002099|2328045122| +++++++++++++++++++++++++++++++++++++++++++++++ ^ ^ ^ ^ | | | | sign length +---------+ | values 

For simplification I don't use only first value of pointer to keep both sign and size.

issues:

• If I use First method, it will waste a lot of memory (e.g. for 18-digit First method needs 20 bytes and Second method needs 16 bytes; the difference will be greater in bigger values).

• Second method needs more calculation if we want print it as decimal.

Questions:
Which method you suggest me to use?
Which method is more similar to that one languages like python use?
Is there any better method?

PS: Yeah, using struct can make it easier, but that's not my point; I just wanna know storing each digit separately is better than storing number based on int's size or not. Please don't refer me to external libraries like GMP. I wanna know what such libraries internally do.