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4 problems, 5 pages Exam One 4 February 2009
Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate the pages of the exam. For maximum credit, show your work. Good Luck!
Your Name ( please print ) ________________________________________________
1 2 3 4 total
Not 110 more weeks of winter!
4 problems, 5 pages Exam One 4 February 2009
Problem 1 (2 parts, 20 points) Switch-level Design
Several incomplete circuits are shown below. Complete each circuit by adding the needed switching network so the output is pulled high or low for all combinations of inputs (i.e., no floats or shorts). Complete each circuit (pull down, pull up, or both) and write the expression if one is not given. Assume both inputs and complements are available.
A D E
B C F
OutX OutY
OUTx =
OUTy = ( A + B โ
C )โ
E โ
F
4 problems, 5 pages Exam One 4 February 2009
Problem 3 (2 parts, 22 points) Boolean Algebra
Part A (10 points) 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 + B )โ
( C + D )โ
E + F โ
G โ
H
Out (^) Y =(( A โ
B + C )โ
D )+( E โ
F )
Part B (12 points) For the behavior described by this truth table, (A) write the sum of products expression using minterms, (B) write the product of sums expression using maxterms, and (C) write the simplified sum of products expression (using any simplification technique).
A B C Out 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0
(A) SOP minterm expression
(B) POS maxterm expression
(C) simplified SOP expression
4 problems, 5 pages Exam One 4 February 2009
Problem 4 (2 parts, 30 points) Karnaugh Maps
Part A (12 points) Given the following Karnaugh Map, circle and list all the prime implicants for a product-of-sums (POS) expression, indicating which are essential. Derive the simplified POS expression.
1 X 1 0
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
simplified POS expression Part B (18 points) For the following expression, derive a simplified sum of products expression using a Karnaugh Map. Circle and list all the prime implicants for a sum-of-products (SOP) expression, indicating which are essential.
Out =( B + D )โ
( A + B + D )โ
( A + B + C )
A
A
B B
C
C
C
D
D D
prime implicants
essential? yes no
simplified SOP expression
