Download Exam Solutions for ECE 2030B Computer Engineering Spring 2010 - Problems 1 to 4 and more Exams Computer Science in PDF only on Docsity!
4 problems, 5 pages Exam One Solutions 10 February 2010
Problem 1 (2 parts, 20 points) Switch-level Design
The three parts below contain (A) a pull up network, (B) a pull down network, and (C) an expression to be implemented. For (A) and (B), complete the missing complementary switching networks so the circuit contains no floats or shorts and write the Boolean expression computed by the completed circuit. For (C), design the entire switching network. Assume the inputs and their complements are available.
(A) (B)
OUTx = (^) A โ
( B + C )โ
( D + E + F ) OUTy = (^) C + D โ
E
OUTz = A^ โ
^ C + B โ
(^ D + E ) (C)
4 problems, 5 pages Exam One Solutions 10 February 2010
Problem 2 (2 parts, 28 points) Mixed Logic Reengineering
For the following expressions, implement the Boolean expression using the specified gate type. Use correct mixed-logic notation. Do not simplify the expression. You may use multi-input gates. Minimize the total transistors (switches) required. When possible, use common subexpressions to reduce gate counts. Also determine the number of switches used in each implementation.
Part A (14 points) Implement A โ
( B + C )โ
( D + E )+( D + E )using only NOR and NOT gates.
switches = (^) 22T
Part B (14 points) Implement A + ( B โ
C + D )+ E โ
F using only AND and NOT gates.
switches = (^) 34T
4 problems, 5 pages Exam One Solutions 10 February 2010
Problem 4 (2 parts, 30 points) Karnaugh Maps
Part A (15 points) Given the following Karnaugh Map, circle and list all the prime implicants for a sum- of-products (SOP) expression, indicating which are essential. Derive the simplified SOP expression.
X
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
1
B C D
A B D
A C D
A C
simplified SOP expression (^) A โ
C + A โ
C โ
D + A โ
B โ
D or A โ
C + A โ
C โ
D + B โ
C โ
D
Part B (15 points) For the following expression, derive a simplified product of sums expression using a Karnaugh Map. Circle and list all the prime implicants, indicating which are essential.
Out =( A + B + C )โ
( A + B + C + D )โ
( A + C + D )โ
( A + B + C + D )โ
( A + B + C )
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
B + C
C + D
A + B + D
simplified POS expression (^) ( B + C )โ
( C + D )โ
( A + B + D )
