In other words, how does the ISFD calculate the air data and IR parameters? Or is the ISFD an ADM by itself?
Standby instruments provide a critical backup function and are totally independent from the primary air data system. The dedicated standby probes are connected directly to the standby display unit which is capable of converting the pressure inputs into airspeed and altitude. They only require a 28V DC input from the EMER/BATT power bus to operate.
Here's the description diagram from the Boeing maintenance manual: