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ec311hw03

# ec311hw03 - EC 311 Introduction to Logic Design Fall 2009...

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EC 311 – Introduction to Logic Design Fall 200 9 Homework Assignment # 3 09/18/09 Due Date: 09/29/09 (in class) *Please show all the steps clearly to receive full credits. (e.g. the final optimized answer, the truth table, the Boolean function, etc.) **You must come up with and write-up the solutions on your own. Identical homework with the same mistakes will be investigated for cheating. 1. (10/100)Problem 1: For the Boolean function F(a,b,c,d)= ab'c + abc'd + abcd + a'bc'd + a'bc'd', determine all prime implicants and all essential prime implicants of the function. 2. (10/100)Problem 2: Use K-maps to obtain the minimized POS (Product-Of-Sums) expressions for X and Y A B C X Y 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 0 3. (20/100)Problem 3: Express the following Boolean functions in a minimized SOP (Sum-Of-Products) form using K-maps. (i) F(A, B, C, D) = Π M(0,2,3,4,6,7,15) * Π D(8,9,11) (ii) F(A, B, C, D) = Σ m(2,3,4,10,11,12) + Σ d(6,14,15) 4. (20/100)Problem 4: Draw the schematics for the following Boolean functions using only the gates specified. The gates can have any number of inputs.

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