Although the mitzva d'oraita is to thank God only when you are satiated from the meal, chazal decreed that we say birkat ha'mazon even when eating only the volume of a k'zayit and even if not satiated. So you must still say birkat ha'mazon after eating at least 1.3 fl. oz. (39 ml, or 1/6 cup) of bread within four minutes--even if you are not full.  This is known as birkat ha'mazon d'rabanan.