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HW2 - ECE2030C FallSemester,2009 HomeworkAssignment#2...

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1. (15%) Use Quine-McClusey Method to simplify the following canonical SOP forms. Identify all Essential Prime Implicants based on the Q-M Method. F ( W , X , Y , Z ) = m (0,3,4,5,7,9,11) + d (8,12,13,14 ) F ( A , B , C , D , E ) = m (0,4,12,15,27,29,30) + d (1,5,9,10,14,16,20,28,31 ) 2. (15%) Implement the following Boolean Expressions using Mixed Logic. For each equation, show two implementations of the logic circuits - one completely in NAND gates and the other completely in NOR gates. Write down how many NAND (or NOR) gates are needed for each logic circuit. Note : Do not simplify the equations. F ( A , B , C , D ) = A B C + D F ( W , X , Y , Z ) = W + X Y + Z W 3. (15%) Timing Diagrams: Using the input waveforms below, sketch the outputs described in each part below. Show the inputs as well as the outputs in each case so that it is clear where each transition occurs. a. Sketch the output F 2 = AB + AC + BC using the input waveforms A, B, and C shown below. b. If A, B, C, and D are the input lines to a 4 x 1 multiplexer (A = input 0), and S1, S0 are the select lines, sketch the output Y.

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• Spring '09
• many
• Binary-coded decimal, 4-bit BCD, sketch outputs D0, following canonical SOP, 4-bit BCD number, 4-bit BCD numbers

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HW2 - ECE2030C FallSemester,2009 HomeworkAssignment#2...

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