Consider a Boolean function F with the following minterm expression:β¦
2026
Consider a Boolean function F with the following minterm expression:
F(π,π,π ,π)= βπ (1,2,3,4,5,7,10,12,13,14)
Which of the following options is/are the minimal sum-of-products expression(s) of F ?
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Show answer & explanation
Construct a K-map for F(P,Q,R,S) with minterms 1, 2, 3, 4, 5, 7, 10, 12, 13, 14.
Identify Prime Implicants (PIs):
- Group 1: m1, m3, m5, m7 -> Term: P'S
- Group 2: m4, m5, m12, m13 -> Term: Q\bar{R}
- Remaining minterms to cover: 2, 10, 14.
- Cover m2: Use PI \bar{P}\bar{Q}R (covers 2,3).
- Cover m10, m14: Use PI PR\bar{S} (covers 10,14).
The minimal SOP is P'S + Q\bar{R} + \bar{P}\bar{Q}R + PR\bar{S}, which matches Option 1.
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