Question

In the combination of the following gates the output Y can be written in terms of inputs A and B as

1- \[\overline{A.B}\]
2- \[A.\overline{B}+\overline{A}.B\]
3- \[\overline{A.B}+A.B\]
4- \[\overline{A+B}\]

Answer 1

Hint: This is the problem of Logic gates. Here we are given five gates and two inputs A and B. We have to apply the logic operation for each gate to arrive at the meaningful answer for each gate and then the final answer.

Complete step by step answer:

WE have numbered the gates as 1,2,3,4,5.
Gate 1 and gate 2 are NOT gates. They invert the input given to them.
Output of gate 1 =\[\overline{B}\]
Output of gate 2= \[\overline{A}\]
Now gate 3 and gate 4 are AND gates. If the input to the AND gate are A & B, then the output Y= A.B
So,
Output of gate 3 = \[A.\overline{B}\]
Output of gate 4 = \[\overline{A}.B\]
Now, the input to gate 5 is \[A.\overline{B}\] and \[\overline{A}.B\]. Gate 5 is the OR gate. If the input to the OR gate are A & B, then the output Y= A+B. So, the output of gate 5 will be, \[A.\overline{B}+\overline{A}.B\].

So, the correct answer is “Option 2”.

Additional Information:
Logic gates are the basic building blocks of any digital system. There are only two inputs to the logic gates. These are 0 and 1 or we can say high and low. They form the backbone of digital integrated circuits.

Note:
In this problem we are not given what are real inputs. But we are given the five gates and we should know the logic operation of each gate in order to arrive at meaningful information. The relationship between the input and the output is based on a certain logic.