Determine the shorthand POS notation for the following reduced SOP function – [Free] B23
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) Π(0,3,5,6,8,12,15) П(0,2,3,7,11,13,15) Π(0,1,3,6,9,12,14) Π(2,3,4,6,9,10,12,15) Π(2,3,4,6,9,11,15) Π(1,3,4,8,11,13,15)
![Determine the shorthand POS notation for the following reduced SOP function - [Free] B23](data:image/svg+xml,%3Csvg%20xmlns='http://www.w3.org/2000/svg'%20viewBox='0%200%20639%20346'%3E%3C/svg%3E)
Answer
🔄 SOP to POS Conversion – Boolean Function Analysis
🟨 Step 1: Analyze the SOP Expression
F = AD′ + A′B′C′ + A′BD + BC′D
🟩 Step 2: Determine Covered Minterms
- AD′: A = 1, D = 0 (B and C are “don’t care”) → minterms: 4, 5, 6, 7
- A′B′C′: A = 0, B = 0, C = 0 (D is “don’t care”) → minterms: 0, 1
- A′BD: A = 0, B = 1, D = 1 (C is “don’t care”) → minterms: 10, 14
- BC′D: B = 1, C = 0, D = 1 (A is “don’t care”) → minterms: 9, 13
Total minterms: 0, 1, 4, 5, 6, 7, 9, 10, 13, 14
🟥 Step 3: Find the Maxterms
For a 4-variable function, there are 16 possible minterms (0–15).
Maxterms (not in SOP): 2, 3, 8, 11, 12, 15
🧾 Step 4: POS Shorthand Notation
F = Π(2, 3, 8, 11, 12, 15)
❌ Step 5: Final Check
None of the given options in the multiple-choice list match the derived POS expression.
Correct Answer: none of these