"Finite$-$State Machine Assignment $($Residential Thermostat$)$:

There are two temperature sensors in a resid TR$11$ ential building $$ an internal sensor and an external sensor$.$ The internal sensor measures the internal temperature, and the external sensor measures the external temperature of the building. There are a central heater and a central AC in the building, both controlled by a thermostat. Now, design and draw the state diagram of this thermostat that works as follows.

$$ If the internal temperature is within $1$ degree of the desired temperature, the thermostat does not change any settings.

$$ If the internal temperature is $1$ degree higher than the desired temperature, the thermostat turns on the AC$.$

$$ If the internal temperature is $1$ degree lower than the desired temperature, the thermostat turns on the heater.

$$ If the external temperature and the desired temperature are within $5$ degrees of each other, the thermostat disregards the internal temperature and turns off both the AC and the heater."