Question

The logic circuit shown below is equivalent to :

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Step 1: Given Data:

Step 2: Determine the circuit output

1. When the input $B$ passed through NOT gate, it produces the output $\overline{B}$.
2. We know that the OR gate add the given input. So, when the combined input $A$ and $\overline{B}$ passed through the OR gate, it produces the output $A+\overline{B}$.
3. Further when the $A+\overline{B}$ passed through the NOT gate, it produces the output $\overline{A+\overline{B}}$.
4. According to Demorgan's Theorem, the complement of the sum of all the terms is equal to the product of the complement of each term. So,$\overline{A+\overline{B}}$ can be written as follows:

$\overline{A+\overline{B}}=\overline{A}B$

Step 3: Determine the correct choice

1. Among all the options, the obtained output matches only with the output of option $B$.

1. When the input A passed through the NOT gate, it produces the output $\overline{A}$.
2. When the combined input $\overline{A}$ and $B$ passed through the AND gate, it produces the output $\overline{A}B$ because AND gate multiplies the given input.
3. So, it is clear that the circuit output matches the output produced by the logic circuit of option B.

Hence option C is the correct answer.