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midterm1_soln

# midterm1_soln - ECE 152A Fall 2006 University of California...

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ECE 152A – Fall 2006 10/19/2006 Midterm Exam #1 – Page 1 of 17 University of California, Santa Barbara Department of Electrical and Computer Engineering ECE 152A – Digital Design Principles Midterm Exam #1 – Solution October 19, 2006 Name _____________________________________ Perm # ____________________________________ Lab Section _______________________________ Problem #1 (20 points) ____________ Problem #2 (20 points) ____________ Problem #3 (20 points) ____________ Problem #4 (20 points) ____________ Problem #5 (20 points) ____________ Total (100 points) ____________ This is a 75 minute exam; closed book, closed notes, no calculators. Answer all questions on the paper provided by the instructor. Write on only one side of the paper. Attach answer sheets to this exam in the correct order. Include your name and perm # on every sheet.

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ECE 152A – Fall 2006 10/19/2006 Midterm Exam #1 – Page 2 of 17 Problem #1. 1. Using only Boolean algebra, convert the following Sum of Products expression to simplified Product of Sums representation. A’B + B’C’D + B’CD + A’C’D
ECE 152A – Fall 2006 10/19/2006 Midterm Exam #1 – Page 3 of 17 2. Again, using only Boolean algebra, convert the following Product of Sums expression to simplified Sum of Products representation. (B’ + C)(A + C’ + D’)(A + B’)(A’ + C’ + D’)

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ECE 152A – Fall 2006 10/19/2006 Midterm Exam #1 – Page 4 of 17 3. Again (and finally), using only Boolean algebra, prove the following theorem: (X+Y)(X’+Z)(Y+Z) = (X+Y)(X’+Z) Problem #2. 1. Map the following sum of minterms function on a Karnaugh map: Σ m = (0,2,5,8,13) + d(10,11,14,15)
ECE 152A – Fall 2006 10/19/2006 Midterm Exam #1 – Page 5 of 17 2. Identify all prime and essential prime implicants and minimize the function.

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midterm1_soln - ECE 152A Fall 2006 University of California...

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