How can I add two strings that contain integer to find the sum?

I try to find the sum of two strings without having to convert to integer like using atoi or stoi It is BigInt class implementation

Example of two strings:

BigInt a("-1000");
BigInt b("+999");

I have a class which private members are:

private:
    string data;
    bool negative;

The purpose of this question is to write a arithmetic operations like +,-,/,*