Yes, there are a couple of things wrong with your class.
(a) The print function prints the value of a newly created variable B, which will be zero all the time. Just use your own member digits instead! Also: Your print functions contains a bug: It just prints the non-zero digits!
(b) The add and subtract member functions don't touch your member digits at all, which doesn't make sense. Instead you might want to provide functions like
void add (const bigint& A);
void subtract (const bigint& A);
which add/subtract A to/from the object the operation is applied to.
(c) Working in decimal digits will not get you the best performance and is a waste of memory. Why don't you work in base 2 and hence use the built-in arithmetic operations. That will increase the performance of your functions by one or two orders of magnitude. Just for the purpose of printing a number it needs to be converted back to decimal.