How Do I Perform Arithmetic Operations On Char

This is not achieved this way. You should have started with your goal.
—SA

Look, I did not want to write about it in my answer, but I feel you are trying to think in a wrong way: using strings representing data instead of data itself.
And the idea to "perform arithmetic operation on char" it especially wrong.

I would understand if you asked about "arithmetic operation" on string, such as
BitInt b("123");
b += 11;
b *= "321";
...
But it would be different thing; and "arithmetic operations on char" would still not be useful. Calculations on strings are quite possible, but this is not how bigInt is usually implemented. The data behind such type is usually binary, say, array of bytes...

But of course, any decent BigInt library should include initialization from string. If such constructor is missing, it's way too easy to add. The library should have such operations as power and multiplication, with operator overloading for bitInt operands and combinations with all CPU integer types. Apparently, the number represented by each decimal character in the string is value * power(10, N), where N is the position of the digit (from right, of course), and value is the numeric value corresponding to the digit (for '2', it's 2, not 50 :-).

—SA