GATE CS 2024 Set 2 — Question 50
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Digital Logic → Boolean Algebra & Logic Gates → Minterms & Maxterms
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Question
Consider 4-variable functions expressed in sum-of-minterms form as given below.
With respect to the circuit given above, which of the following options is/are CORRECT?
Correct answer
(C) Y = Σ(0,1,2,3,4,5,6,7); (D) Y = (8,9,10,11,12,13,14,15)
Solution
The circuit consists of an AND gate, an OR gate, and an XOR gate.
The intersection of minterms is:
The union of minterms is:
The XOR operation includes minterms present in or but not both (Symmetric Difference).
Minterms in :
Minterms in :
Common minterms ():
Union ():
Removing common minterms from the union:
So, in sum-of-minterms form:
This matches Option (C).
The missing minterms from the set are .
Therefore, .
This matches Option (D).Thus, both (C) and (D) are correct representations of the function .
1.Top Branch (AND gate):
Let the output of the AND gate be .The intersection of minterms is:
2.Bottom Branch (OR gate):
Let the output of the OR gate be .The union of minterms is:
3.Final Output (XOR gate):
The XOR operation includes minterms present in or but not both (Symmetric Difference).
Minterms in :
Minterms in :
Common minterms ():
Union ():
Removing common minterms from the union:
So, in sum-of-minterms form:
This matches Option (C).
4.Product-of-Maxterms Form:
The maxterms correspond to the minterms not present in the function.The missing minterms from the set are .
Therefore, .
This matches Option (D).Thus, both (C) and (D) are correct representations of the function .
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