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To get an output \[Y = 1\] in a given circuit which of the following input will be correct?

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

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Last updated date: 24th Feb 2024
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IVSAT 2024
Answer
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Hint: For AND gate to give the output as one, the two inputs must be equal to one too. For an OR gate to give the output as one, only one of the inputs is necessary to be equal to 1, the other can either be one or zero.

Complete Step-by-Step Solution:
In the given logic circuit, we see that an OR gate is connected to one of the inputs of an AND gate, and another input is connected to the AND gate, and the result is 1. We are asked for the possible values of the input A B C amongst the given options.
To solve, let’s go through the options one after the other.
For option A, we have \[A = 1\], \[B = 0\], \[C = 1\]
Investigating this, A and B are connected to an OR gate. the output of the OR gate is 1 if at least one of the inputs is 1. Hence, the output at the OR gate is 1. This means that the input at one of the AND gates is 1.
Now, the input C is also equal to 1. This means that the two inputs of the AND gate are both equal to 1.
For the output of an AND gate to be equal to 1, the two input must be equal to one. Hence, the output of the AND gate is indeed equal to one, which is Y

Hence, option A is correct.

Note: Alternatively, without having to investigate one after the other or go through lengthy procedure, we can observe that the value of C in all other options is 0. Since, the AND gate cannot be 1 if at least one input is 0, then these options must be wrong, and option A must be correct.