Consider 4-variable functions f1, f2, f3, f4 expressed in sum-of-minterms form…
2024
Consider 4-variable functions f1, f2, f3, f4 expressed in sum-of-minterms form as given below.
f1 = ∑(0,2,3,5,7,8,11,13)
f2 = ∑(1,3,5,7,11,13, 15)
f3 = ∑(0,1,4,11) f4 = ∑(0,2,6,13)
With respect to the circuit given above, which of the following options is/are CORRECT?
- A.
𝒀 = ∑(0,1,2,11,13)
- B.
𝒀 = Π(3,4, 5,6,7,8,9,10,12,14,15)
- C.
𝒀 = ∑(0,1,2,3,4,5,6,7)
- D.
𝒀 = Π(8,9,10,11,12,13,14,15)
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Correct answer: C, D
Solution:
Evaluate the two intermediate signals and then the XOR:
a = f1 AND f2 = intersection of f1 and f2 = {3,5,7,11,13}.
b = f3 OR f4 = union of f3 and f4 = {0,1,2,4,6,11,13}.
Y = a XOR b = symmetric difference = {0,1,2,3,4,5,6,7} = ∑(0,1,2,3,4,5,6,7).
Equivalently, Y = Π(8,9,10,11,12,13,14,15) since those are exactly the minterms where Y = 0.
Quick check: for minterm 3, f1=1 and f2=1 so a=1; f3=0 and f4=0 so b=0; Y = 1 XOR 0 = 1, so 3 must be included—confirming the ∑(0..7) result.
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