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4 problems, 5 pages Exam One 15 September 2008
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
Binary Racer
4 problems, 5 pages Exam One 15 September 2008
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.
Outy A
B
C
D
Outx
A B
D E
C
Outz
A
B
C
OUTx =
OUTy =
OUTz =
4 problems, 5 pages Exam One 15 September 2008
Part B (8 points) Write the Boolean expression intended by the designer in for the mixed logic circuit below. Also determine the number of switches required for this implementation.
A
B
D
E
OUTY
OUTZ
C
F
OUTY =
OUTZ =
transistors =
Part B (10 points) Now reimplement this behavior using more efficient multi-input NOR gates and inverters. Your design must properly employ mixed logic methodology. Determine the number of switches required for this improved implementation.
transistors =
4 problems, 5 pages Exam One 15 September 2008
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 + D )โ
( A + B + C )โ
( A + B + C + D )
A
A
B B
C
C
C
D
D 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 = C โ
D + A โ
B โ
C + B โ
C โ
D
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
simplified POS expression
