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The instructions and problems for an exam in computer engineering (ece 2030) held in fall 2002. 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 reengineering, playing with blocks, and karnaugh maps.
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4 problems, 5 pages Exam One 18 September 2002
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 18 September 2002
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
B D
C
Out x
E
no dot!
A
D
B
Out y
E
C
Out z A B
D
C
E
OUTx =
OUTy =
OUTz =
4 problems, 5 pages Exam One 18 September 2002
Problem 3 (2 parts, 20 points) Playing with Blocks
Part A (10 points) Consider the following circuit. For each combination of inputs listed below, describe the corresponding outputs.
oops!
In 0
In 1
En
Out 0
Out 1
Out 2
Out 3
In 0
In 1
In 2
In (^3) In 3 > In 2 > In 1 > In 0
Out 0
Out 1
C V
Part B (10 points) Implement a 2 to 4 decoder using basic gates (AND, OR, NAND, NOR, and NOT). Assume you have the inputs (In0, In1, En) and their complements. Gates can have any number of inputs.
4 problems, 5 pages Exam One 18 September 2002
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 B โ C + B โ C + A โ B 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 + D )โ ( A + B + D )โ ( A + B + C + D )
prime implicants
essential? yes no
simplified SOP expression
