Recall that na, used as an adverb, roughly translates to already.
Thus your sentence I am hungry should translate to Gutom ako. The reverse translation of Gutom na ako is I am already hungry.
Similarly, Hindi ako gutom translates to I am not hungry. The reverse translation of Hindi na ako gutom is I am no longer hungry.
In both English and Tagalog this would be more colloquially expressed as I'm full (Busog ako / Busog na ako / Busog na busog ako).