Nice!, I think understand... well, I would put, for example, the number 1234567890 in a[0] = '1', a[1] = '2', a[3] = '3', and so on and the number 987654 in b[0] = '9', b[1] = '8', and so on.
After, I would convert each number in position to integer and I would operate separately. For example, convert a[n] and b[n] character number to integer number and operate; converting the result in character storing in tmp[i]. And son on to each position on the vector. Final tmp, is the number result after some operation. It`s correct?