C/C++ :: Fastest / Most Efficient Way To Add Two Fractions

I have to write a function

struct rNumber add(rNumber a ,rNumber b); 

which adds two rational numbers in following representation :
rNumber := s*(n/d)* 2^e
struct rNumber{
 _byte_t s; // sign (do not consider for this question)
 uint n; //numerator
 uint d;// denominator
 short e;//exponent
}  

If the exponents of both numbers are not equal, then they have to be made equal in order to add them. This can be made in 4 ways : increase or decrease the n or d of both numbers.

But if we decrease the denominator of a number (a.d =1) by shifting it for example 1 bit to the right, we get 0 which leads to INFINITY for the fraction. In another case decreasing the numerator would lead the n to be 0 which meanse the whole fraction is then 0.

According to this, in worst case, all 4 cases has to be checked for the right result.

So far the UNDERFLOW of n or d is considered. If we try to increase the value of n or d, then OVERFLOW may also occur.

The very first, intuitive solution would be iteratively increase/decrease one of the terms and to check if the change leads to ZERO or INFINITY.