You are given the two circuits as shown in the figures. Show that circuit (a) acts as OR gate while the circuit (b) acts as AND gate.

Home » You are given the two circuits as shown in the figures. Show that circuit (a) acts as OR gate while the circuit (b) acts as AND gate.

You are given the two circuits as shown in the figures. Show that circuit (a) acts as OR gate while the circuit (b) acts as AND gate.

Solution:

(a) Input for the circuit: $A$ and $B$

Output for the circuit: $Y$

The left part of the circuit functions as a NOR gate, while the right half of the circuit functions as a NOT gate.

We can show it in the figure as:

Now, the output for the NOR gate will be $\overline{A+B}$

We are giving the output from NOR gate to the input at NOT gate. So, its output will be: $\overline{\overline{A+B}}=\mathrm{A}+\mathrm{B}$

$\therefore Y=A+B$

Hence, we proved this circuit functions as an OR Gate.

(b) Input for the circuit: $A$ and $B$

Output for the circuit: $Y$

The output from the first half of the circuits passes to the input of the second half, which acts as a NOR gate, as shown in the below figure:

Hence, the output of the given circuit can be written as:

$Y=\overline{\bar{A}+\bar{B}}=\overline{\bar{A}} \cdot \overline{\bar{B}}=A \cdot B$

Hence, we proved this circuit functions as an AND gate.

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