Question
You are given the two circuits as shown in figure. Show that circuit (a) acts as OR gate while the circuit (b) acts as AND gate.
Solution
(a) Here,
In figure (a) input A and B is applied to NOR gate. So the output of NOR gate is Y’.
Truth table is given below:
In figure (a) input A and B is applied to NOR gate. So the output of NOR gate is Y’.
Truth table is given below:
|
A |
B |
Y’ |
|
0 |
0 |
1 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
0 |
Now Y’ is feeded as input into NOT gate.
So output Y is represented in form of truth table as shown.
|
Input Y’ |
Output Y = Y’ |
|
1 |
0 |
|
0 |
1 |
|
0 |
1 |
|
0 |
1 |
which is similar to the truth table of OR gate.
The boolean expression for the circuit is as follows:
which is the expression for OR gate.
(b) Here in figure (b), input A and B are given to two NOT gates and these inverted input is provided to NOR gate.
Its truth table can be represented as:
|
Output of NOT gats |
|||
|
A |
B |
Ā |
|
|
0 |
0 |
1 |
1 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
0 |
1 |
|
1 |
1 |
0 |
0 |
Now output of NOT gate is fed as input to NOR gate. So its truth table can be represented as:
|
Input |
Output |
|
|
Ā |
Y |
|
|
1 |
1 |
0 |
|
1 |
0 |
0 |
|
0 |
1 |
0 |
|
0 |
0 |
1 |
which represents AND operation.
The boolean expression for circuit (b) is:
which the expression for AND gate.
