What happens if we add denormalized number and normalized number?

Denormalized numbers can represent numbers smaller than 2^(-1022) whereas normalized number cannot. So I'm curious what happens if we add denormalized number and normalized number. Actually, I have tried some tests and it seems that the computer converts denormalized number to 0. Is my thought correct?

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.