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in Physics by (15 points)
1.      Reduce the following functions using Karnaugh Maps (K-Maps):

a) (, , , ) = ∑ (5, 7, 8, 13, 14, 15) in Sum of Products (SOP).    [4 Marks]

b) (, , , ) = ∐ (0, 1, 2, 3, 4, 8, 12) in Product of Sums (POS).   [4 Marks]

c) Draw the logic diagrams of the expressions obtained in Q1(b) above.

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