Prove or provide a counter example If the pairwise product of all prime implicants of f is 0 then it has a unique minimal expression.
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Prove or provide a counter example
If the pairwise product of all prime implicants of f is 0 then it has a unique minimal expression.
Step by step
Solved in 2 steps
- Prove that f(x) = x is O(x3).b) Find the minimum sum of products SoP using K-map for: f(A, B,C, D) = IT M (0,2,6,7,9,12,13) • II D(1,3,5). Note that 1,3,5 are don't care termsExplain what is Euler number o(m) for a natural number m > 1. Give a proof of Euler Theorem, whose proof you could write down straightforward by generalising that of Fermat little Theorem. (cf. the handout on Moodle Topic 12).
- 3. Use a K-map to find a minimal expansion as a Boolean sum of Boolean products of the of the function F(x, y, z) = x + yx of the Boolean variables x and y.For the function f(w,x,y,z) = E (m4, m7, m8, m9, m10, m12, mi13, m15), complete the parts of this question below. (a) Draw and fill in a correct, properly-labelled Karnaugh map for f(w,x,y,z). (b) List ALL sum-of-prod. prime implicants, and identify which ones are essential. (c) Write the complete least-cost sum-of-products expression for f(w,x,y,z). (d) Now consider m2, m5, and m11 as don't-care cases for f(w,x,y,z) in part (a). Provide the least-cost sum-of-products expression using this information.Problem 2 Simplify the given Boolean function f in product-of- sums form (POS) by using a map. f(A, B,С,D,E) 3D Zm(0, 1 , 4, 5, 16, 17, 21, 25, 29) Clearly label all groups accordingly and show all grid lines on maps.