Why does a GCU have an integer counter, does it need to count something to measure time or cycles of something?
That's a question for the hardware guys.
I'm not working with areospace, but in my field of engineering (wind turbines) it differently would have integer counters.
Often those systems run at a constant scan rate, and software filters and timers are used to slow down the reaction of the system in a configurable manner.
Since systems have boxes connected together with communication links, monitoring of broken communication links have to be implemented. (Typical as
Timeouts).
Another purpose could be for shutting tings down in case of faults, e.g. stop the engine if the lubrication pressure is lower than 2 bars for 5 secs.
Timers is also used to delay, and prevent erratic state change of an output, i.e. prevent a valve from being turned off/on every 10ms. Scan.
(Persistent) Counters are also used for statistics for maintenance and trouble shooting.
It is good system-engineering practice to separate/compartmentalize safety critical control, from datalogging for diagnostics.
If all modern computers are coded in 64 bit sizes, why did Boeing stick with 32 bit
The size of a counter value is primary related to software, and not hardware architecture.
Using a 64bit desktop microprocessor in such an environment is often a bad idea, if possible micro-controllers like ARM cortex is used instead.
A bigger complex CPU use more power, generates more heat, and is 100 times more unreliable than a small microcontroller.
An Intel desktop CPU is only on the market for 3 years, and industrial/aerospace products have to be supported for 20 years.
Some of the newer micro controllers like the TMS570 have features that make safety certification easier.