GATE CS 2024 Set 1 — Question 47
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Consider a Boolean expression given by .Which of the following statements is/are CORRECT?
Correct answer
(A) F(X, Y, Z) = (0,1,2,4); (B) F(X, Y, Z) = XY + YZ + XZ
Solution
Given the Boolean function in Sum of Minterms (SOP) form:Analysis of Option (A):
The function is defined over 3 variables, so the total minterms range from 0 to 7. The maxterms correspond to the minterms that are not present in the function.
Missing minterms: .
Thus, the Product of Maxterms (POS) form is:This statement is CORRECT.Analysis of Option (B):
Let's simplify the function using the minterms:
This statement is CORRECT.Analysis of Options (C) and (D):
The expression depends on all three variables. For instance:
These statements are INCORRECT.
The function is defined over 3 variables, so the total minterms range from 0 to 7. The maxterms correspond to the minterms that are not present in the function.
Missing minterms: .
Thus, the Product of Maxterms (POS) form is:This statement is CORRECT.Analysis of Option (B):
Let's simplify the function using the minterms:
- ()
- ()
- ()
- ()
- Group :
- Group :
- Group :
This statement is CORRECT.Analysis of Options (C) and (D):
The expression depends on all three variables. For instance:
- If , then . The output depends on .
- If , then . The output depends on .
These statements are INCORRECT.
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