Given f(w, x, y, z) = Σₘ(0,1,2,3,7,8,10) + Σ_d(5,6,11,15), where d represents…
2017
Given f(w, x, y, z) = Σₘ(0,1,2,3,7,8,10) + Σ_d(5,6,11,15), where d represents the don’t-care condition in Karnaugh maps.
Which of the following is a minimum product-of-sums (POS) form of f(w, x, y, z)?
- A.
f = (w' + z') (x' + z)
- B.
f = (w' + z) (x + z)
- C.
f = (w + z) (x' + z)
- D.
f = (w + z') (x' + z)
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Correct answer: A
Identify maxterms where f=0 by excluding minterms and don't-cares. The zeros are at indices 4, 9, 12, 13, and 14. Plot these on a Karnaugh map to group zeros with don't-cares into the largest possible rectangles.
Combine the groups to form sum terms. For example, grouping 4, 6, 12, and 14 yields the term (x' + z). Ensure all maxterms are covered to derive the minimum product-of-sums expression.
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