The way the moon "works" is that the time it rises and its fullness slowly change together (because the reason it looks "full" or "half" or whatever is because of its position relative to the earth and the sun, which also determines when it's visible) until at the full moon it rises shortly after sunset and sets shortly before sunrise.

Therefore, the full moon is NEVER visible during the day. Conversely, the full moon lasts the entire night.

(Actually, it turns out that this NEVER must be qualified slightly. At latitudes close to 66.5 degrees, occasionally this might happen very briefly. See http://curious.astro.cornell.edu/question.php?number=341 for details.)