Correct (I was mixing up the “1:00:00” display with a display of “0:00:00”). If it shows 1:00:00 it would be impossible (in theory) to have any tenths of a second showing. The “tenths of a second” (if it even were possible to display them) would only matter if the display read “0:00:00” (in which case if it were possible to show tenths of a second, that would prove that there is a fraction of a second left before two hours is used up).
Even better - if the clock says 0:00:00 AND that you are still in the first time control, then you know that there IS a fraction of a second (not displayed) still to go - and the flag is UP.
Reviewing: when the clock says 1:00:00, the flag is DOWN but when the clock says 0:00:00 the flag is UP.
Crystal clear.
A bit more opaque.
A Chronos allows for the possibility of the clock displaying 1:00:00 at the end of two hours (indicating that exactly one hour remains, and that exactly two hours has elapsed).
But I believe some other clocks (maybe the Excalibur, for example?) do not allow for a display of 1:00:00 remaining. They just show a countdown from 0:00:02 then 0:00:01 then 0:00:00 then 0:59:59, etc. When it shows “0:00:00” that means the non-displayed fraction of a second is “0” (indicating the entire 2 hours has elapsed), becasue there is no display of 1:00:00 (indicating that exactly one hour remains). The closest you get is a display showing that less than one hour remains (0:59:59).
If the clock does not have a display of 1:00:00 at the end of the first time control, that would mean that the flag is down at 0:00:00.
The seconds won’t display until the delay has counted down. In fact the delay is indicated with a blinking cursor moving up and own. It won’t will display 1:00 unless the player kept the move counter going for both controls. I have seen players do that. The TD would have to let the delay count down to see if it says 1:00:00 or 1:00:xx xx=seconds left from 1st control.
If it’s gone down to 00:00:00 before the 40th move has been completed, it will stay there until the side presses the clock. (This happens when halt at end is set to 0. Halt at end set to 1 the clock will stay at 0:00 with the move counter displayed.) Then it will say 1:00:00. That would indicate to me that the side whose clock now says 1:00:00 most likely forfeited. I played around with it. Once 40 moves happens it resets and keeps going. If white had 1 second left from the first time control when he made his 40th the display would read 1:00:01. If he didn’t, the display would show 1:00:00.
I don’t have much pity for a player who has to ask an opponent to stop a digital clock. Digital clocks are so common place now, that unless my opponent is a newbie playing in his very first tournament I’m going to assume he knows how to stop my Chronos. If he doesn’t then he should ask. If he’s provided the clock then I’m going to assume he knows how to stop it.
I used to use the move counter, but I had a couple of incidents recently that got me thinking that using it wasn’t a good idea. Reading this thread has totally convinced me. 
Digital clocks (all of them, as far as I know) round seconds upwards. Thus, if it shows 1:23:45, there is somewhere between 1:23:44 and 1:23:45 remaining. Similarly, if it shows 1:00:01 or 0:00:01, there is somewhere between 0 and 1 seconds remaining. Therefore, if it shows 1:00:00 or 0:00:00, time has expired, period.
If you don’t believe this, set your digital clock for 4 minutes (0:04:00) with no delay, start it, and watch it sit there for a full second before it goes to 0:03:59. (I picked 4 minutes as the starting time so that even the Saitek, which won’t show seconds until below 5 minutes, can be used to demonstrate this point.)
The hours digit makes no difference, if it’s just there because of a 2nd time control of 1 hour.
There could be a problem if the clock is not displaying seconds. Minutes, unlike seconds, are rounded downward. So a display of 1:00 (one hour) could mean either 1:00:00 or 1:00:ss, where ss>0. Therefore, if the clock added an hour prematurely (because the move counter was wrong), it could be important to determine the value of ss. Fortunately, on the Chronos, this is easy – just stop the clock and go into mid-game adjustment mode. (Long-press the center button, once on the newer models, 3 times on the older models.) Go through the digits one by one, and it will eventually display the seconds.
Bill Smythe