The text states that a truth table or equivalent is the starting point for traditional combinational minimization methods. A Karnaugh map itself contains the same information as a truth table. Given a sum-of-products expression, it is possible to write the Is corresponding to each product term directly on the map without developing an explicit truth table or minterm list, and then proceed with the map- minimization procedure. In this way, find a minimal sum-of-products expression for each of the following logic functions:
(a) F = X′ ⋅ Z + X ⋅ Y + X ⋅ Y′ ⋅ Z
(b) F = A′ ⋅ C′ ⋅ D + B′ ⋅ C ⋅ D + A ⋅ C′ ⋅ D + B ⋅ C ⋅ D
(c) F = W′ ⋅ X ⋅ Z′ + W ⋅ X ⋅ Y ⋅ Z + W′ ⋅ Z
(d) F = (W′ + Z′) ⋅ (W′ + Y′ + Z′) ⋅ (X + Y′ + Z)
(e) F = A′ ⋅ B′ ⋅ C′ ⋅ D′ + A′ ⋅ C′ ⋅ D + B ⋅ C′ ⋅ D′ + A ⋅ B ⋅ D + A ⋅ B′ ⋅ C′
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