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Main points of this exam paper are: Behavior Below, Maximum Credit, Computer Engineering, Logic Design, Mixed Logic Design, Design Style, Gates and Inverters, Switch Circuits, Product of Sums, Prime Implicants
Typology: Exams
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4 problems, 5 pages Exam One 5 February 2003
Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate the pages of the exam. For maximum credit, show your work. Good Luck!
Your Name ( please print ) ________________________________________________
1 2 3 4 total
4 problems, 5 pages Exam One 5 February 2003
Problem 1 (3 parts, 27 points) Incomplete Circuits
For each partial switch circuit below, complete the complementary switching network so the circuit contains no floats or short. Also write the Boolean expression computed by the completed circuit. Assume the inputs and their complements are available.
A
D
B
Out y
E
C
F
Out z A B
D
C
E
A
B D
C
Out x
E
OUTx =
OUTy =
OUTz =
4 problems, 5 pages Exam One 5 February 2003
Part C (10 points) Reimplement the behavior below with a mixed logic design style using only NAND gates and inverters. Determine the number of switches used in this implementation.
Problem 3 (3 parts, 18 points) Switch-Ready Expressions
Transform each of the following boolean expressions to a form where they can be implemented using switches (i.e., there should be no bars in the expression except for complements of the inputs A, B, C, etc.). The behavior of the expression should remain unchanged. There is no need to design switch circuits in this problem; just transform the expressions.
Out (^) X = A โ B + C + D + E
Out (^) Y = A + B + C + D + E
Out (^) Z =( A + B )โ ( A โ B )โ ( A โ B + A โ B )
4 problems, 5 pages Exam One 5 February 2003
Problem 4 (2 parts, 26 points) Karnaugh Maps
Part A (13 points) For the follow expression, derive a simplified product of sums expression using a Karnaugh Map. Circle and list the prime implicants, indicating which are essential.
Out = A โ C โ D + A โ B โ D + B โ C โ D + A โ B โ C โ D
prime implicants
essential? yes no
simplified POS expression Part B (13 points) For the follow expression, derive a simplified sum of products expression using a Karnaugh Map. Circle and list the prime implicants, indicating which are essential.
Out =( A + B + D )โ ( B + C + D )โ ( A + B + D )โ ( A + C + D )โ ( A + B + C + D )
prime implicants
essential? yes no
simplified SOP expression
