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4 problems, 4 pages Exam One Solutions 6 February 2002
Problem 1 (3 parts, 27 points) Switch Design
For each expression below, create a switch level implementation using N and P type switches. Assume both inputs and their complements are available. Your design should contain no shorts or floats. Use as few transistors as possible.
A
B
Outx A
C
D
B C
D
A
B Outy
C
D
A B
C D
Out z A
B
C
A (^) B
C
OUTx = A + B โ
C + D OUTy = A โ
B + C โ
D OUTz = A โ
B + C
4 problems, 4 pages Exam One Solutions 6 February 2002
Problem 2 (3 parts, 27 points) Mixed Logic Reengineering
A B C D E F OUTx
OUTy
Part A (9 points) Write the output expression for the gate design shown above. Also determine the number of switches used in its implementation. OUTx = (^) A + B โ
C + D OUTy = (^) C + D + E โ
F
switches = (3) x 6 + (2) x 4 + (6) x 2 = 38
Part B (9 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.
A B C D E F OUTx
OUTy
switches = (5) x 4 + (5) x 2 = 30
Part C (9 points) Reimplement the behavior below with a mixed logic design style using only NOR gates and inverters. Determine the number of switches used in this implementation.
A B C D E F OUTx
OUTy
switches = (5) x 4 + (5) x 2 = 30
4 problems, 4 pages Exam One Solutions 6 February 2002
Problem 4 (2 parts, 26 points) Karnaugh Maps
Part A (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 โ
B โ
D + A โ
B โ
C + B โ
C โ
D + A โ
C โ
D + A โ
B โ
D
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
A D
A C
B D
C D
C + D
simplified SOP expression (^) B โ
D + A โ
C + C โ
D
Part B (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 + C + D )โ
( A + B + C )โ
( A + C + D )โ
( A + B + C + D )
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
A + B + C
A + D
simplified POS expression (^) ( C + D )โ
( A + D )โ
( A โ
B โ
C )
