GATE EE 2024 Set 1 — Question 24
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Analog & Digital Electronics → Digital Logic Circuits → Boolean Algebra & Gates
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Question
Simplified form of the Boolean function is
Correct answer
(A) PS + QS
Solution
Given Boolean function:Step 1: Simplify the last two terms using the distributive law:So, .Step 2: Use a K-map to find the prime implicants. The minterms are:
- covers cells 0, 1, 2, 3.
- covers cells 5, 7.
- covers cells 8, 10.
- Group 1 (cells 1, 3, 5, 7):
- Group 2 (cells 0, 2, 8, 10):
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