It is not that "part of the nucleon's mass is converted to energy" ; it is that in an interacting system, the total mass of the overall system is not just the sum of the (rest) masses of the components, it is rather, the sum of the rest masses of the components minus the mass equivalent of the binding energy.
It is because we tend to think that the overall mass is the sum of the masses of the constituents, that we seem to have a "missing mass". This sum rule is a good approximation as long as binding energies have negligible mass equivalents, such as is often the case in chemistry. But it isn't generally true.
So, again, not "part of the nucleon's mass" is converted to energy. It is simply that the mass of the overall system is NOT equal to the sums of the masses of the free constituents.