My periods of amnesia were drug-induced, most significantly when I had been given Midazolam as a pre-med prior to surgery, and prior to my pre-op consult with my surgeon. I woke up from my GA shouting that I couldn't go in for my surgery yet because I hadn't had my pre-op consult. It is still extremely strange to me that I had a 15 minute conversation with my surgeon and consented to the specifics of my procedure and yet have no memory whatsoever of this consult. It's made me more careful as a physician to ensure that my patients are capable of consenting.

You would be able to feel that time had passed, even if you randomly napped during the day. You may initially be slightly confused as to how much time had passed or what day it was, but you would be aware that that you had been sleeping. This varies among people but many people mark time so accurately while sleeping that they do not need to set alarms (whether or not the alarm is routine).