Please explain step by step to obtain the state machine that solves the following exercise, with the following steps:

$1.$ Perform the State Assignment

$2.$ Perform the State Variable Declaration

$3.$ Perform the State Map

$4.$ Determine the Next State Calculation Logic

$5.$ Determine the Output Calculation Logic

A control unit must be designed for the water supply system shown in the simulation.

The system is used to supply pressurized water through a hydropneumatic tank that is fed by pumps B$1$ and B$2$ from a supply tank. The input signal system to the control consists of three sensors$,$ one for the upper water level in the tank and two for pressure in the tank. The level detector is activated

when the upper level is reached and is released only when it falls below that level. The pressure detectors PB and

PMB are activated when the low pressure and the very low pressure are reached respectively, and are released only

when the normal pressure is reached.

Once the tank is full, its water level $($and therefore the pressure$)$ begins to fall due to external

demand. When the pressure decreases to PB$,$ pump B$1$ is activated, which will turn off when the upper water level is reached

$($full tank$).$ Again the tank begins to lose water level and when PB is reached, pump

B$2$ is activated. As long as PB continues to be reached under these conditions, the pumps will continue to alternate indefinitely.

However, if when starting operation it happens that the external demand is greater than the water supplied to the tank, its level, and therefore, its pressure will decrease even more. Under these circumstances, when the pressure

PMB is reached, the idle pump must be activated to support the active pump. Both will be turned off when the upper water level is reached. This action must not alter the alternation order of the pumps and therefore, the next pump to be turned on will be the one that acted as a backup.

It will be assumed that the water supply provided by the simultaneous action of the two pumps exceeds the demand

and in that case the upper level will always be reached.

Suppose that TLL $($full tank$),$ PB $($low pressure$)$ and PMB $($very low pressure$)$ are active signals in logic $1$