In $64-$bit computers, the maximum value that a signed integer variable can represent is $2^{63}-1,$ while an unsigned integer variable can represent a maximum value of $2^{64}-1.$ In other words, integer variables can only represent numbers with the length smaller than $64$ bits in binary system. If we want to get the addition result of two integers with $100$ bits of binary system like $"1010$dots$1110"$ and $"1001..\mathrm{.}1011"($which are too large and can only be stored in string variables$),$ the original addition operation of computers can not be used. Please design an algorithm to implement the addition of two string variables with more than $100$ bits for each. $(12\text{'})$