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4 problems, 4 pages Exam One Solutions 15 September 2004
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.
B
C D
Out x
A
Outy A
B E
C
D
F
A
B D
Outz
E
C
no dot (^) E
A
D
B
E
C
A B C D E F
A B
C D
OUTx = ( A + D )โ
( B + E )+ C
OUTy = A โ
B โ
C โ
D โ
E โ
F
OUTz = A โ
B + C โ
D
4 problems, 4 pages Exam One Solutions 15 September 2004
Problem 2 (3 parts, 26 points) Mixed Logic Design
Implement the following expressions to minimize total transistors (switches) required. Where two expressions are specified for a single part, your implementation should provide both outputs. Use proper mixed logic design technique. Any combination of Two, three, and four input AND, OR, NAND, NOR, and NOT gates may be used. Do not simplify the expression. Part A (6 points) OUT (^) X = A โ
B + C โ
D + E โ
F
B C
E F
D OUTx
A
switches = 3 x 4 + 1 x 6 = 18T
Part B (8 points) OUTY = A โ
B + C โ
D
A B
C
OUTy
D
switches = 3 x 4 + 1 x 2 = 14T
Part C (12 points) OUTZ 1 (^) = A โ
B + C , OUTZ (^) 2 = B + C + D + E
A
B C
E
OUTZ
D OUTZ
switches = 2 x 4 + 1 x 6 + 3 x 2 = 20T
4 problems, 4 pages Exam One Solutions 15 September 2004
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 โ
B + A โ
C โ
D + 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
A C
A D
simplified SOP expression (^) A โ
B + C โ
D + A โ
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 =( A + B + C + D )โ
( A + B + C )โ
( A + C + D )โ
( B + C )
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
B + D
B + C
A + B
A + C + D
A + B + C
simplified POS expression (^) ( A + B )โ
( B + C )โ
( A + B + C )โ
( B + D )
