Question

An AND gate is followed by a NOT gate in series. With two inputs $A$ and $B$, the Boolean expression for the output $Y$ will be:

• A. $A·B$
• B. $A+B$
• C. $\overline{A+B}$
• D. $\overline{A·B}$

Answer 1

The correct option is D

$\overline{A·B}$

Explanation for the correct option:

Step 1: Given data.

1. In the question, it is given that an AND gate is followed by a NOT gate in series.
2. The input is $A$ and $B$.
3. $Y$ is the output of the combination.

Step 2: Concept to be used.

1. When $p$ and $q$ are the input of AND gate, then the output can be represented as $p·q$.
2. According to the definition of NOT gate, The output of NOT gate is the negation of the input which means if the input is false then the output is true and if the input is true output is false.
3. When $p$ is the input of the NOT gate, then the output can be represented as $\overline{p}$.

Step 3: Find the Boolean expression for the output $Y$.

Initially, two inputs $A$ and $B$ are given to the AND gate.

Assume that, the output of the AND gate is $Y\text{'}$.

Therefore, the output of the AND gate is given by: $Y\text{'}=A·B$.

Since The AND gate is followed by a NOT gate in series combination. So, the output of AND gate will be the input of the NOT gate.

So,

$$\begin{gathered} Y=\overline{Y\text{'}} \\ \Rightarrow Y=\overline{A·B} \end{gathered}$$

Therefore, the Boolean expression for the output Y will be $\overline{A·B}$.

Hence, option $D$ is the correct answer.