Can you prove or provide a counter example for:f a function f has a unique minimal sum-of-products expression then it also has a unique minimalproduct-of-sums expression
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Can you prove or provide a counter example for:
f a function f has a unique minimal sum-of-products expression then it also has a unique minimal
product-of-sums expression
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Solved in 2 steps
- Karnaugh maps and standard forms.For this function:F (A,B,C,D)= Σm (0,1,2,5,8,9,10) Do the following: 1-) Write the minimal function in product-of-sums formKarnaugh maps and standard forms.For the following function:? (?, ?, ?, ?) = Σ? (0,1,2,5,8,9,10)1-) Write the minimal function in product-of-sums formSimplify the following expressions to sum of products and products of sums using K-map: (a) wyz + xyz' + wxy Subject DLD Give solution
- ---SIMPLIFICATION VIA KARNAUGH MAPS (K-MAPS)--- Each of these problems starts with a truth table which you may need to complete. From there, you need to write an unoptimized sum-of-products formula, where each product corresponds to a single 1 in the output of the table, and all the products are summed together. You will then use a K-Map to simplify the formula on paper, and then write out the simplified formula in this file. 2.) Given this truth table, find the unoptimized formula this corresponds to, along with the version which was optimized with a K-Map. A B C | O 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 Unoptimized Sum of Products equation 2a) 0 = Draw the K-map and simplify Optimized Sum of Products equation 2b) 0 =Find all prime implicants and all minimum sum-of-products expressions and all minimum product-of-sums for the following functions. 1. f(A,B,C,D) = Em(3,4,11,15) + E d(5,6,7,8,9,10) %3! 2. f(A,B,C,D) = Em(4) + E d(5,6,7,8,9,10,11,12,13,14)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.
- not handwritten Use K-maps to simplify function f and it’s don’t care condition below. Perform the reduction for (a) the sum-of-products form and (b) the product-of-sums form.f(w, x, y, z) = ∑ m(2, 8, 10, 11) + ∑ d(0, 9)K-Map drawingQ4/ Given the Boolean function F(A, B, C, D) =(0, 1, 6, 7, 1O, 11) together with the don't care conditions d (A, B,C,D)= (2,3,4,5,8,9,14,15). a) Simplify F in sum of products (SOP). b) Simplify F in product of sums (POS). c)implement the function f in both
- 7.) Given the following Truth Table for the function F, generate a Karnaugh-Map for the function F (1 Point), and a Boolean Algebra representation of the function F (1 Point). Each variable (A,B,C,D) and its complement (Ā,B, C,D) are available as an input if needed. I provided a blank K-Map template to save you time. A BC D F 1 0 0 01 0 01 0 0 0 1 1 0 10 0 0 1 0 1 0 11 0 01 1 |1 10 0 0 10 0 1 1 0 1 1 10 10 1 |1 110 0 1 10 1 11 1 0 1 1 1 1 1 1Make K-map as follows10. Use a three-variable Karnaugh Map to find the minimum sum-of-products for the Boolean function: F(A,B, C) = Dm(0,1,3,5,6,7). 11. Use a four-variable Karnaugh Map to find the minimum product-of-sums for the Boolean function: F(A, B,C,D) = Em(0,4, 6, 12,14) +Ea(1,3,5,8, 9).