C bigint datatypes

Instead of defining datatypes with preset sizes for big integers in C (like GMP and other libraries do), why not define operations on them for arbitrarily sized character arrays so that you can define how large you want your integer to be?

The problem is, you'll implement your BigInts a way or another depending on what you do with them.
If you want to print them often (in base 10), using base 10^9 in int32_t may be a good idea, whereas if you want to print this shit in hexa or binary, a regular implementation like >>13 is better.