@KingAir1978:
The only reason the ISIS is also connected to ADIRU 1/3, is for the temperature, so it can calculate a Mach number.
Mach calculation is derived from Pitot and Static pressure, no need to supply a separate Temp. signal.
ISIS initializing can take 90 sec. during this period airspeed is supplied by ADIRU 1/3 depending on position of ATT/HDG selector switch.
@Emergency000:
I believe the ISIS also has its own dedicated battery.
Back-up power supply is BAT HOT BUS, no separate dedicated battery involved.