1. 24-hour clock system
00:00:00 - 23:59:59
2. 12-hour clock system
12:00:00 am - 11:59:59 am
12:00:00 pm - 11:59:59 pm
no 00:00 am or 00:00 pm, it should be 12 midnight or 12 noon
It is incorrect to write 0:00p.m. The use of 0:00 implies a 24-hour clock system, while the use of A.M. and P.M. implies a 12-hour clock system. Therefore, it is absolutely wrong to use both together.
The 12-hour clock divides the day into two parts, 12 hours each. The middle of the day (midday) is the twelfth hour, noon, or the meridiem. A.M. refers to the hours prior to midday (Latin: ante meridiem) while P.M. refers to the hours after midday (Latin: post meridiem). Since the meridien is thought to occur right at the exact second of the 12th and 24th hours, it is most common to hear the times referred to as 12 noon or 12 midnight, rather than using a.m. or p.m. However, to be clear, 12:01p.m. refers to the time just after (post) the 12th hour, that is, the first minute after midday (noon); while 12:01a.m. refers to the first minute of the new day, therefore prior to (ante) midday, that is, just after midnight (after the 24th hour of the previous day).