GATE EE 2025 Set 1 — Question 37
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Analog & Digital Electronics → Digital Logic Circuits → Boolean Algebra & Gates
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Question
A Boolean function is given as
The simplified form of this function is represented by
The simplified form of this function is represented by
Correct answer
(A) [figure]
Solution
The given Boolean function is:
Let .
Let , , , .The expression can be rewritten as:
Using the distributive law repeatedly:
First, consider
Next, consider
Now, multiply these two simplified terms:
Substitute back :
This simplified Boolean function represents an OR gate with inputs and .Option (A) shows an OR gate where the input is first inverted to and then fed into the OR gate along with . This matches the simplified expression .The final answer is .
Let .
Let , , , .The expression can be rewritten as:
Using the distributive law repeatedly:
First, consider
Next, consider
Now, multiply these two simplified terms:
Substitute back :
This simplified Boolean function represents an OR gate with inputs and .Option (A) shows an OR gate where the input is first inverted to and then fed into the OR gate along with . This matches the simplified expression .The final answer is .
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