Download Exam Solution for ECE 2030 Computer Engineering Fall 2006 - Problem 1 to 4 and more Exams Computer Science in PDF only on Docsity!
4 problems, 4 pages Exam One Solution 20 September 2006
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.
Out x
A
B C
D E
A B D
C E
Out y A
B
E
C
D
C
A
B
D
E
Outz
A C
B D
A
C
B
D
OUTx = A โ
B โ
D + C โ
E
OUTy = ( A + B โ
D + E )โ
C
OUTz = ( A + C )โ
( B + D )
4 problems, 4 pages Exam One Solution 20 September 2006
Problem 2 (2 parts, 20 points) Mixed Logic Design
Implement the following expressions using gates 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 multi-input input AND, OR, NAND, NOR, and NOT gates may be used. Do not simplify the expression.
Part A (8 points) OUTX = A โ
B + C โ
D + E โ
F
A B C D E F
OUTX
switches = 5 x 4 + 2 x 2 = 24T
Part B (12 points) OUTY = A โ
B + C โ
D , OUTZ = C โ
D + E
A B C D E
OUTY
OUTZ
switches = 4 x 4 + 2 x 2 = 20T
4 problems, 4 pages Exam One Solution 20 September 2006
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
C โ
D + A โ
B โ
D + B โ
C + A โ
C โ
D + A โ
B โ
C โ
D
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
B C
C D
A C
A B D
A B C
simplified SOP expression (^) A โ
C + B โ
C + A โ
B โ
C + C 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 + C + D )โ
( A + C + D )โ
( A + C )โ
( B + C + D )
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
A + D
C + D
C + D
A + C
simplified POS expression (^) ( C + D )โ
( C + D )โ
( A + C )or ( C + D )โ
( C + D )โ
( A + D )
