Determine the shorthand POS notation for the following reduced SOP function – [Free] B40
Determine the shorthand POS notation for the following reduced SOP function of just its maxterms. F=AD’ A’B’C’ A’BD BC’D Π(2,3,4,6,8,11,15) П(0,3,5,6,8,12,15) П(0,2,3,7,11,13,15) П(0,1,3,6,9,12,14) П(2,3,4,6,9,10,12,15) П(2,3,4,6,9,11,15) Π(1,3,4,8,11,13,15) none of these П(0,2,5,7,11,12,15) Π(0,2,3,4,9,11,12)
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Conversion from SOP to Shorthand POS Notation
Determine the shorthand POS notation for the following reduced SOP function of just its maxterms:
F = AD′ + A′B′C′ + A′BD + BC′D
Step 1: Identify the minterms represented by each product term.
- AD′ → A=1, D=0 →
minterms: 8, 9, 10, 11 - A′B′C′ → A=0, B=0, C=0 →
minterm: 0 - A′BD → A=0, B=1, D=1 →
minterms: 5, 7 - BC′D → B=1, C=0, D=1 →
minterms: 5, 13
Step 2: Collect all unique minterms where the function is true.
Minterms = {0, 5, 7, 8, 9, 10, 11, 13}
Step 3: Determine all 4-variable combinations (0–15) and identify the maxterms.
Total minterms = 0 to 15 (i.e., 16 values)
Maxterms = All − Minterms
⇒ Maxterms = {1, 2, 3, 4, 6, 12, 14, 15}
⇒ Maxterms = {1, 2, 3, 4, 6, 12, 14, 15}
Step 4: Write the shorthand POS notation using Π (capital pi) symbol.
F = Π(1, 2, 3, 4, 6, 12, 14, 15)
This is the compact representation of the function in Product of Sums (POS) format based on its maxterms.
✅ Final Answer:
Π(1, 2, 3, 4, 6, 12, 14, 15)