This answer is highly suspect and should be independently verified. Also, it only talks about the timers and the Master Timing Unit:
The computers themselves:
- The IBM System/4_PI architecture was used as the system architecture for the AP101 source
- The timer feature on this system was a full word (so, presumably 32 bits) Source, but not a primary source
- The timer counted down with the clock frequency, but unfortunately I don't know what that was
The Master Timing Unit
This was the thing that held all of the information about MET and so on. It also was used for synchronization of the 4 + 1 AP101 computers on board. It was an atomic clock and was read by each AP101 once per second to make sure that the AP101s' clocks stay in sync. source
It also held the MET stuff, which was stored in its accumulators (sorry, I don't know the number of bits). This timing information was stored in days, hours, minutes, seconds, and milliseconds, up to one year until it overflowed. I do not know if that means MET was stored as days as well as hours etc, or as days/hours/minutes, nor do I know whether there were multiple accumulators. source
I'm interested in knowing more about the answers, so I provide my answer in the hopes that someone else can fill in the details.