[abacate]

I don't see how this reasoning makes any sense: you just need to look at the actual clock time to find out if the alarm went off or not.

For instance: alarm set for 8 AM.

You wake up, look at the clock: if it says 7:59AM or earlier, you woke up before it had a chance to ring. If it says 8:00AM or anything past that, it already went off.

Unless, of course, you have an alarm that does not show you the current time. Otherwise, it's pretty easy to figure out what's happening.