Exact Waking

I am confused by this. One night ago, I was horribly jet-lagged from my trip to Japan (16 hour time difference.) I went to bed at 4:00 PM and woke up at 9:24 PM. I went to sleep again at 11:30 and woke up at 9:24 AM. I went back to sleep and woke up at 11:24 AM. Why is my waking time exactly at the 24th minute of every hour? Also, when I set my alarm for 7:00 AM, let's say, I usually wake up at 6:58 or 6:59, as though my brain can sense what time it is, or something. I am also a long sleeper, so this doesn't make sense. Any possible explanations?

We have an "internal clock" that helps us wake up at a specified time. Waking up a few minutes before an alarm is set to go off is not uncommon.

As for waking on the 24th minute, I think that's just a koinkedink. ;)