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The instructions and problems for an exam in computer engineering (ece 2030 b) held in fall 2004. The exam consists of 4 problems, and students are not allowed to use books, notes, or calculators. The problems cover topics such as incomplete circuits, mixed logic design, switch-ready expressions, and karnaugh maps.
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4 problems, 5 pages Exam One 15 September 2004
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 15 September 2004
Problem 1 (3 parts, 30 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.
B
C D
Out x
A
Outy A
B E
C
D
F
A
B D
Outz
E
C
no dot (^) E
OUTx =
OUTy =
OUTz =
4 problems, 5 pages Exam One 15 September 2004
Problem 3 (2 parts, 20 points) Switch-Ready Expressions
Part A (12 points) Transform each of the following Boolean expressions to a form where they contain only AND operations. The behavior of the expression should remain unchanged.
Out (^) X = A โ B + C โ D + E + F
OutY = A โ B + C โ D + E + F
Part B (8 points) Using the following Karnaugh map definition of a behavior, specify each donโt care and identify prime implicants for a product of sums expression, indicating which are essential.
prime implicants
essential? yes no
4 problems, 5 pages Exam One 15 September 2004
Problem 4 (2 parts, 24 points) Karnaugh Maps
Part A (12 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 โ B + A โ C โ D + A โ B โ D + A โ B โ C โ D
prime implicants
essential? yes no
simplified SOP expression Part B (12 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 + B + C + D )โ ( A + B + C )โ ( A + C + D )โ ( B + C )
prime implicants
essential? yes no
simplified POS expression
