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4 problems, 4 pages Exam One Solutions 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
C
Outx
E
no dot!
A
E
B
C
D
D
A
D
B
Out y
E
C
A C
B
E
D
A
B Outz A B
D
C
E
C
D
E
OUTx = ( A + E )โ
B + C โ
D
OUTy = ( A โ
C + B )โ
( E + D )
OUTz = A โ
B + C + D โ
E
4 problems, 4 pages Exam One Solutions 18 September 2002
Problem 2 (3 parts, 27 points) Mixed Logic Reengineering
A B C D E F OUTx
OUTy
OUTz
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
OUTz = ( C + D )โ
( E + F )
switches = 5 x 6 + 6 x 2 = 30 + 12 = 42
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
OUTz
switches = 5 x 4 + 4 * 2 = 20 + 8 = 28
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
OUTz
switches = 5 x 4 + 7 x 2 = 20 + 14 = 34
4 problems, 4 pages Exam One Solutions 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
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
A + B
C + D
B + C
simplified POS expression (^) ( A + B )โ
( C + D )โ
( B + C )
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 )
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
B D
C D
A D
A B C
A B D
simplified SOP expression (^) B โ
D + A โ
D + A โ
B โ
D + C โ
D
