Question
You are given two circuits as shown in figure, which consist of NAND gates. Identify the logic operation carried out by the two circuits.
Solution
The truth table for first circuit:
(a)
|
A |
B |
Y’ |
Y |
|
0 |
0 |
1 |
0 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
1 |
If we remove the intermediate output Y’, the overall result stands for the AND gate.
|
A |
B |
Y |
|
0 |
0 |
0 |
|
0 |
1 |
0 |
|
1 |
0 |
0 |
|
1 |
1 |
1 |
Hence, the combinational circuit is equivalent to AND gate.
The truth table for second circuit:
(b)
|
A |
B |
Ā |
Y |
|
|
0 |
0 |
1 |
1 |
0 |
|
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
1 |
|
1 |
1 |
0 |
0 |
1 |
If we remove the intermediate output Ā and , the overall result stands for the OR gate.
Truth table for the OR gate is:
|
A |
B |
Y |
|
0 |
0 |
0 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
1 |
This can be represented as Y = A + B
Hence, the circuit is an equivalent OR gate.
