For the given map find the minimum product of sums.
2018
For the given map find the minimum product of sums.
- A.
(a + b̄ + c)(a + c̄ + d)(b̄ + a)
- B.
(a + b̄ + d)(a + d̄ + c)(b̄ + a)
- C.
(a + b̄ + d)(a + d̄ + c)(ā + b)
- D.
(a + b̄ + c)(a + c̄ + d)(ā + b)
Attempted by 21 students.
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Correct answer: D
To find the minimum Product of Sums (POS), group the 0s in the K-map, using don't-care cells where useful. The vertical pair at ab = 01 with cd = 00 and 01 gives (a + b̄ + c). The horizontal pair at cd = 10 with ab = 00 and 01 gives (a + c̄ + d). The full column ab = 10, using the don't-care cell, gives (ā + b). Therefore, the minimum POS is (a + b̄ + c)(a + c̄ + d)(ā + b), which is option D.