Water level control system.

Water level control systems, as the name suggest are used to monitor the level of water in  a tank.This is one of the basic problems involving the theory of computation and can be solved using a digital circuit.
Consider a tank with water filled to some level .Two switches S1and S2 are used to monitor the level of water in the tank.

When water is below both S1 and S2 ie S1=0 and S2=0,the motor has to be switched on to fill the water.
When the water level is above the S1,we have S2=1 and S2=1.Now the motor is turned off.
When water is in between the switches that is S2=1 and S1=0 then the motor has to remain in its earlier state that is if motor is on then it remains in on state and in off state otherwise.
The state S1=0 and s2=0 is an invalid case and does not exist
The truth table for the same can be formed as..
                                           
                                      S1              S1            Previous state       Output

                                       0                0                       x                        1
                                       0                1                       0                        0
                                       0                1                       1                        1
                                       1                1                       x                        0
                     
A simple circuit can be designed using a NOR gate XNOR gate and a D flip flop .The flip flop is used to retain the previous state of the motor.The logic used is once the water is below S1 and S2 ,then the motor is turned on until the water is filled to the max that is above both the switches.Now the motor is turned off until the water drains below both S1 and S2..after with the motor is turned on again.
The circuit for the same can be designed as....