What happens if we add denormalized number and normalized number?
The result depends on the difference between the normal and denormal numbers you are adding.
 $1 + [denormal]$ is rounded to $1$.

But if the range difference between your numbers is inferior to $2^{52}$ for doubles, or $2^{23}$ for singles, you will get a real addition. There is nothing special about denormals here : $1 + 2^{-200}$ is rounded to $1$ as well.

To implement a floating point adder (as hardware or software), you shift right the smaller number to equalize the exponents before doing an integer addition to the aligned mantissas. If the range difference is too large, the smaller number is entirely shifted out.