Question

For the given logic diagram, output  \[F = 1\] , then inputs are:

A) \[A = 0,B = 0,C = 0\]
B) \[A = 0,B = 1,C = 0\]
C) \[A = 1,B = 1,C = 1\]
D) \[A = 0,B = 0,C = 1\]

Answer 1

Hint: In this solution, we will find the logic equation for the output of F. A and B terminals are connected to an OR gate while C is connected to a NOT gate.

Complete step by step answer:
As given in the image, we can see that A and B are connected to an OR gate.
This gives an output of $A + B$
The C terminal is connected to a NOT gate which gives us output $\bar C$
Both these gates are then connected by an AND gate so the net output would be
$F = \left( {A + B} \right).\bar C$
For the output F to be 1, we can see that both of the inputs of the final and gate must be one. Hence for the input coming from the C terminal to be 1, the input of C must be zero i.e. $C = 0.$
For the input coming from the A or B gate, either A or B must be one. From the options, we can see that the only option satisfying the above conditions is option (B).
The configuration \[A = 0,B = 1,C = 0\] will give an output of 1 in the following way. The combination of A OR B will give a 1 since $B = 1$. The output of $\bar C$ will be 1 since the input of C is zero.
Hence the combination of both inputs of the AND gate is 1 so the final output will also be 1.

Hence the correct choice is option (B).

Note: In such questions, it is helpful to check all the options one by one to determine which set of inputs will give the output of 1. So we must be aware of the output table of different kinds of logic gates to answer this question.