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# A building has two overhead water tanks, each fitted with a sensor (S1, S2) which goes when the water level in the tank is below a set value and remains 1 otherwise. A common pump is used to raise water from an underground storage tank to these overhead tanks of the following circuits, which one will turn on $\left( P=1 \right)$ the pump only when at least one of the tanks has water below the set value ?(A) (B) (C) (D)

Last updated date: 04th Mar 2024
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Hint: Automatic water-level controller for overhead tanks that switches on/off the pump motor when water in the tank below/above the minimum/maximum level. The water-level is sensed by two floats to operate the switches by two floats to operate the switches for controlling the pump motor. This water controller is mainly made up of logic gates. Generally, we have three basic logic gates: (1) AND gate (2) OR gate (3) NOT gate.
AND gate (MULTIPLICATION): The AND gate is a circuit which provides an output when all the inputs are simultaneously present. Mathematically, we can write $A.B=X$
OR gate (ADDITION): The output voltage is high if any or all of the input voltages are high. Mathematically, we can write $A+B=X$
NOT gate: The NOT gate is a gate with only one input and one output. It is called so because the output state is always opposite to that of input state i.e., if input is 0, then output is 1 and if input is 1, then output is 0. Mathematically, we can write $X=\overline{A}$ .
We will solve the above problem by using gate expressions.

Complete step by step answer
As in our problem, two overhead water tanks, each filled with sensors (S1, S2) which goes when the water level in the tank is below a set value and remains 1 otherwise. A common pump is used to raise water from an underground storage tank to these overhead tanks of the above circuits. We have to find out which one will turn on the pump only when at least one of the tanks has water below the set value.
That means one of the values of the sensor is 1 and the value of another sensor is 0.
Now, we will check each circuit one by one. Consider first option,
Consider, S1=1 and S2=0
When these inputs go to AND gate output of the first gate will be 0 and output of the second gate is also zero. Now, the output of AND gate is the input of OR gate. The output from OR gate is 0 because the Boolean equation for OR gate is $A+B=X$ . Therefore this option is wrong.

NOW, consider second option, we have S1=1 and S2=0
When it goes to the first gate the output will be 0 and when it goes to the second gate the output will be 0. These are input for the gate. Output for both NOT gates will be 1 because the Boolean algebra for NOT gate is $X=\overline{A}$ . Then the input for OR gate from (1) AND gate is 1 and from (2) AND gate is 1. Then, the final output is 1 because the Boolean algebra for OR gate is $A+B=X$ .

So, this is the correct option.
Try out other circuits to find out the value output p.
Option (B) is correct.

Note
Remember the Boolean equation for basic gates. Don’t confuse yourself with Boolean equations. Sensor is an electronic device that measures physical attributes such as temperature, pressure, distance, speed, torque, acceleration, etc. Sensors are central to industrial applications being used for process control, monitoring, and safety. Sensors are also central to medicine being used for diagnostics, monitoring, critical care, and public health.