GATE CS 2025 Set 2 — Question 43
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Given the following Karnaugh Map for a Boolean function :
Which one or more of the following Boolean expression(s) represent(s) ?
Correct answer
(A) wxyz + wxyz + wxyz + wxyz + xz; (D) xz + xz
Solution
From the given Karnaugh Map, we identify the minterms where the function is 1:Row 00 ():
Option (A) expands the term into its canonical minterms with respect to and :Adding the term, we get exactly the expression in Option (A). Thus, Option (A) is also correct.Checking Option (B):
Contains (minterm 11, 1011), which is 0 in the K-map. Incorrect.Checking Option (C):
Contains minterms 0, 8, 10 but misses minterm 2 (). Incorrect.Therefore, options (A) and (D) are correct.
- Column 00 (): 1
- Column 10 (): 1
- Column 01 (): 1
- Column 11 (): 1
- Column 01 (): 1
- Column 11 (): 1
- Column 00 (): 1
- Column 10 (): 1
1.Corners (0, 2, 8, 10): In these cells, and . This group simplifies to .
2.Center Block (5, 7, 13, 15): In these cells, and . This group simplifies to .
Thus, the simplified Boolean expression is:This matches Option (D).Checking Option (A):Option (A) expands the term into its canonical minterms with respect to and :Adding the term, we get exactly the expression in Option (A). Thus, Option (A) is also correct.Checking Option (B):
Contains (minterm 11, 1011), which is 0 in the K-map. Incorrect.Checking Option (C):
Contains minterms 0, 8, 10 but misses minterm 2 (). Incorrect.Therefore, options (A) and (D) are correct.
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