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4 problems, 5 pages Exam One Solutions 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.
OUTx = ๎ ๎ A ๎ B ๎ ๎ C^ ๎ยฐ๎^ D ๎ ๎ E^ ๎
OUTy = ๎ ๎ A ๎ B^ ยฐ ๎ D ๎ยฐ C
OUTz = C
Outx
Outz
A
B
C
A B
D E
C
A
B
C
D
E
Outy A
B
C
D
C
A
B
D
C
4 problems, 5 pages Exam One Solutions 15 September 2008
Problem 2 (1 part, 18 points) Switch-Ready Expressions
Transform each of the following Boolean expressions to a form where they are ready for switch level implementation (i.e., there should only be bars over input variables, not over operations). The behavior of the expression should remain unchanged. Do not implement.
Out (^) X = A โ
B + C + D ๎๎ ๎ A ๎ B ๎ยฐ ๎ C ๎๎ ๎ D =๎ ๎ A ๎ B ๎ยฐ ๎ C ๎ ๎ D
OutY = A + B + C โ
D ๎ ๎ A ยฐ^ B^ ๎๎๎ C ๎ ๎ D ๎= ๎ A ยฐ^ B ๎ C ๎ ๎ D
Out (^) Z = A โ
B + C ๎ A^ ยฐ^ B ยฐ C
Problem 3 (3 parts, 28 points) Mixed Logic Design
Part A (10 points) Implement the following expression using multi-input NAND gates and inverters to minimize total transistors (switches) required. Use proper mixed logic design technique. Do not simplify the expression.
OUT (^) X = A + B + C +( D + E )โ
F
switches =^22
A
B
D
E
C OUT X
F
4 problems, 5 pages Exam One Solutions 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 )
simplified SOP expression ๎ B^ D ๎ ๎ C^ D ๎ A^ D ๎ 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
simplified POS expression ๎^ B ๎ ๎ C^ ๎ยฐ๎ ๎ A ๎ ๎ D ๎ยฐ๎ ๎ D ๎ C^ ๎
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
AB
C D
B D
A D
A C
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
C + D
A + D
B+ C
B + D
