GATE EE 2026 Set 1 — Question 45
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Analog & Digital Electronics → Digital Logic Circuits → Boolean Algebra & Gates
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Question
The digital circuit shown has 3 inputs (, , and ). The simplified logical expression for the output (OUT) is:
Correct answer
(B) 0
Solution
Let's trace the output of each gate in the given digital circuit:
Consider the first term:
Since and , this term becomes:
.Consider the second term:
Since and , this term becomes:
.Adding the two simplified terms:
.The simplified logical expression for the output is .The final answer is
1.NOR gate: Inputs are . The output of the NOR gate is .
Using De Morgan's theorem, .2.NOT gate: Input is . The output of the NOT gate is .
3.First AND gate: Inputs are and the output of the NOT gate (). The output of this AND gate is .
4.Second AND gate: Inputs are and . The output of this AND gate is .
5.OR gate: Inputs are the outputs of the first AND gate () and the second AND gate (). The output of the OR gate is .
6.Third AND gate (final output): Inputs are the output of the NOR gate () and the output of the OR gate ().
So, .Now, let's simplify the expression for OUT:Consider the first term:
Since and , this term becomes:
.Consider the second term:
Since and , this term becomes:
.Adding the two simplified terms:
.The simplified logical expression for the output is .The final answer is
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