The Alarm:
Yes, it is supposed to come ON if 30*5 pertubations have occurred during the one hour after the system was last reset.
Yes, the one hour alarm and one minute timer are separate, but are occurring at the same time. The reason why the one minute period is important is because the 30 pertubations must occur in a one minute period. However, I want the alarm system to be activated when those 30 pertubations in one minute have occurred 5 times in one hour. In other words, the system starts and both one hour and one minute timers would start, with the one minute timer being the time base for the counter and when COUNT>30, pass signal to light LED and also to increment the hour time period based counter.
Ok, try this. Suppose you build a 555 always-running non-gated oscillator (astable) which runs at 136.53 Hz (period is 0.00732sec). You use that to clock a 13 bit binary up-counter, such that on the 8192nd clock, the counter resets for one clock period, and then starts counting again. This produces a gating signal (GATE) which is high for 60sec, and is low for 7msec. I help you do this.
You use this to gate the accelerometer events into their respective counters (Event Counters). They count while the GATE is high; they reset when GATE goes low. The Event Counter is a special counter that counts 0 to 31, but stays at 31 (i.e. it doesn't overflow back to zero) if it gets more than 31 counts during GATE.
There is a decoder on the Event Counter that is true if the value is either 30 or 31. On the high to low transition of GATE, if the decode is true, you increment the Alarm Counter. It takes a four input AND gate to do this decode.
You need another counting chain which creates the one-hour interval. Use the trailing edge of GATE to increment a counter capable of counting to sixty. This could be implemented as a decade counter followed by an octal counter, where you decode "six" in the octal counter. In other words, the one hour interval ends when the count rolls from 59 to 60. It takes a 4 input AND gate to do this. Call the output of this decoder HOUR.
The Alarm counter is a three bit counter as you drew it, except that is has to count up to 5 and then hold at 5 even if more pulses come in. It will take a decode of this counter to detect state 5 so you can arrest it from counting higher. You also use this same decode to sound the alarm horn.
The RESET button resets all of the counters to initialize everything for a new cycle.
btw- this is entirely too much damn work. I would have put all of this logic inside a PIC in the same time as we have been discussing it...