Question

A) You are given the circuit as shown in figure. Show that circuit acts as OR gate.

B) You are given the circuit as shown in figure. Show that circuit acts as AND gate.

Answer 1

A) Given,
Input for the circuit, A and B
Output for the circuit, Y
In the given circuit the left one is NOR gate and the right one is NOT gate.

Output for the NOR gate $=\overline{A+B}$
$\overline{A+B}$ is input for the NOT gate,
Output for the NOT gate $=\overline{\overline{A+B}}$
This will be output for the circuit
$Y=\overline{\overline{A+B}}$
$Y=A+B$
$\begin{array}{cc}\text{INPUTS}& \text{OUTPUT}\\ AB& Y\\ 00& 0\\ 01& 1\\ 10& 1\\ 11& 1\end{array}$
Therefore, the circuit act as OR gate.
Final answer: The circuit act as OR gate.

B) Given,
Input for the circuit, A and B
Output for the circuit, Y
In the given circuit the left two is NOT gate and the right one is NOR gate.


Output for the NOT gate = $\overline{A}$ and $\overline{B}$
$\overline{A}$ and $\overline{B}$ are inputs for the NOR gate.
Output for the NOR gate = $\overline{(\overline{A}+\overline{B})}$
This will be output for the circuit
$Y=\overline{(\overline{A}+\overline{B})}$
$Y=\overline{\overline{A}}.\overline{\overline{B}}$
$\begin{array}{cc}\text{INPUTS}& \text{OUTPUT}\\ AB& Y\\ 00& 0\\ 01& 0\\ 10& 0\\ 11& 1\end{array}$
Therefore, the circuit act as AND gate.
Final answer: The circuit act as AND gate.