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The number of product terms in the minimized sum-of-product expression obtained through the following K = map is (where, "d" denotes don't care states)
| 1 | 0 | 0 | 1 |
| 0 | d | 0 | 0 |
| 0 | 0 | d | 1 |
| 1 | 0 | 0 | 1 |
Answer & Solution
Answer: Option
A
Solution:
Step 1: Identify minterms
From the K-map, the given 1’s (valid minterms) are at positions:
Top row: 1st and 4th cell
Third row: 4th cell
Bottom row: 1st and 4th cell
Step 2: Consider don’t cares (d)
The don’t care cells can be grouped as 1’s if it helps in minimizing the expression.
Step 3: Perform grouping in K-map
- Group all four corner 1’s together. This forms one large group of four.
- Group the remaining 1’s (along with a don’t care if needed) into the second group to cover the leftover minterms.
Step 4: Resulting product terms
After minimization, only 2 product terms
Conclusion
The minimized SOP expression contains 2 product terms.
Therefore, the correct answer is Option A: 2.
From the K-map, the given 1’s (valid minterms) are at positions:
Top row: 1st and 4th cell
Third row: 4th cell
Bottom row: 1st and 4th cell
Step 2: Consider don’t cares (d)
The don’t care cells can be grouped as 1’s if it helps in minimizing the expression.
Step 3: Perform grouping in K-map
- Group all four corner 1’s together. This forms one large group of four.
- Group the remaining 1’s (along with a don’t care if needed) into the second group to cover the leftover minterms.
Step 4: Resulting product terms
After minimization, only 2 product terms
Conclusion
The minimized SOP expression contains 2 product terms.
Therefore, the correct answer is Option A: 2.
