Question

The truth table for the circuit given in the figure is:

(A)\left| \begin{array}{*{35}{l}} A~~~B~~~~~Y \\\ ~0~~~~0~~~~~1 \\\ ~0~~~~~1~~~~1 \\\ ~1~~~~~0~~~~0 \\\ ~1~~~~~~1~~~0 \\\ \end{array} \right|
(B)\left| \begin{array}{*{35}{l}} \text{ }A~~B~~\text{ Y} \\\ ~0~~~0~~\text{ 0} \\\ ~0~~~1~~\text{ 0} \\\ ~1~~~0~~\text{ 1} \\\ 1~~~~1~~\text{ 1} \\\ \end{array} \right|
(C)\left| \begin{array}{*{35}{l}} A~~~~B~~~~~~Y \\\ ~0~~~~~0~~~~~~1 \\\ ~0~~~~~1~~~~~~0 \\\ 1~~~~~~0~~~~~~0 \\\ ~1~~~~~~1~~~~~0 \\\ \end{array} \right|
(D)\left| \begin{array}{*{35}{l}} A~~~~B~~~~~~Y \\\ ~0~~~~~0~~~~~~1 \\\ ~0~~~~~1~~~~~~1 \\\ ~1~~~~~~0~~~~~~1 \\\ ~1~~~~~~1~~~~~1 \\\ ~ \\\ \end{array} \right|

Answer 1

The key to solving problems of this form involving logic gates is to identify the gates that are being used. The first gate used in the question given above is the OR gate. The second gate used in the question is the NAND gate. We need to take the input given by A and B through the first gate and then put back the result of the first gate along with input A into the second gate to obtain the result in the form of output Y.

Complete step by step solution:
Identification of the two logic gates is the first task in this problem. The first gate used here is the OR gate and the second gate used is the NAND gate. We need to be aware of the truth tables of both logic gates to be able to solve this problem.
The truth table of the OR gate is given as follows:

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	1

Likewise, the truth table for NAND gate is given as follows:

A	B	Output
0	0	1
0	1	1
1	0	1
1	1	0

Combination of both the gates gives us the output as follows:

A	B	Output 1	Output 2 = Y
0	0	0	1
0	1	1	1
1	0	1	0
1	1	1	0

Hence, we have the truth table for the given logic gates in the question above for the inputs A and B, giving us the output Y as follows:
\left| \begin{array}{*{35}{l}} \text{ }A~~B~~\text{ Y} \\\ ~0~~~0~~\text{ 1} \\\ ~0~~~1~~\text{ 1} \\\ ~1~~~0~~\text{ 0} \\\ 1~~~~1~~\text{ 0} \\\ \end{array} \right|
Therefore, the correct answer for this question is Option (A).

Additional Information: Besides the OR and AND gates, many other logic gates are available to use. They perform in different ways giving different sets of outputs. Some commonly used logic gates are AND, OR, NOT, NOR, NAND, EXOR, etc.
Note: The major task in this problem is identifying the logic gate from its symbol and writing down the truth table for it correctly. For problems involving more than one logic gate, the output of one gate becomes the input of the next gate and so on to give the final resulting output. The symbols of the logic gates and their performances along with their truth tables must thus be kept in memory.