Its possible your example is wrong and the confusion arises in the "twelves" (i.e. 1230 AM being 0:30 which makes no sense since anyone that didn't learn the qu

Its possible your example is wrong and the confusion arises in the "twelves" (i.e. 1230 AM being 0:30 which makes no sense since anyone that didn't learn the quirk would expect the AM/PM bit to roll over at the same time as the hours, not one hour off the mark).