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ECE · Q41

Digital Electronics

Engineering and GATE · ECE · question 41

Q41

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

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
A.
2
Answer
B.
3
C.
4
D.
5

Answer: Option A

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.