Question

A building has two overhead water tanks, each fitted with a sensor $\left(S_{1} \text{,} S_{2}\right)$ which goes to $0$ when the water level in the tank falls 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 when at least one of the tanks has a water level below the set value?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

As in our problem, two overhead water tanks, each filled with sensors $\left(\left(S_{1}\right)_{,} S_{2}\right)$ which go 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 the first option,
Consider, $S_{1}=1$ and $S_{2}=0$
When these inputs go to $AND$ gate output of the first gate will be $0$ and the 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 the second option, we have $S_{1}=1$ and $S_{2}=0$
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 $OR$ 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 $I^{\text{st}}$ AND gate is $1$ and from $II^{\text{nd}}$ $AND$ 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.