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6 problems Exam One September 27, 1999
Name: ____________________________________
Student ID# ________________________________
This exam is closed notes, closed book, and CALCULATORS ARE NOT PERMITTED. Show all work and place answers in the space provided. If more work space is needed, please use the back of the test sheet and make a note of this next to the problem number. Partial credit will only be given to work that is presented in a clear and structured manner.
Problem Number (Total Points) Points Awarded Problem #1 (20pts) Problem #2 (20pts) Problem #3 (20pts) Problem #4 (5pts) Problem #5 (15pts) Problem #6 (20pts)
Total Points: ________________
6 problems Exam One September 27, 1999
Problem 1 (20points)
a) (10 points) Simplify the following Boolean expression using Boolean Algebra. Please show each step to receive full credit.
F= ( A + AB ) + A ( A + B )
b) (10 points) Using the simplified expression obtained in part (a), draw the CMOS circuit for the resulting logic operation.
6 problems Exam One September 27, 1999
Problem 3 (20pts)
(a) ( 10points) For the following behavior (in map format), derive a simplified sum of products. Circle and list all prime implicants, indicating wheich are essential. Then write the simplified SOP.
Simplified SOP expression: ___________________________________
(b) ( 5 points) For the following k-map, derive a simplified sum of products
Simplified SOP expression: __________________________ (c) ( 5 points) For the following k-map, derive a simplified sum of products
Simplified SOP expression: ________________________________________
X = don’t care condition
AB
CD
Prime Implicants
Essential?
Yes No
00 01 11 10
00
01
11
10
AB
CD
1 0 0 1
0
0 0 0
(^0 0 )
0
1 0 0 1
00 01 11 10
00
01
11
10
AB
CD
0 X 1 0
1
0 0 X
(^0 1 )
0
1 0 0 1
6 problems Exam One September 27, 1999
Problem 4 (5 points): For the following CMOS circuit and the given values of the inputs, please indicate the state of each transistor (i.e. put “on” for conducting and “off” for non-conducting by each nfet and pfet ). Also show a conducting path that connects the output to GRD or Vdd. BE SURE TO FILL IN THE OUTPUT IN THE BELOW TABLE!!
A B C D E OUTPUT
V dd Logic “1”
Logic “0”
GRD
A
B
C
D
E
A
B C
D E
F
6 problems Exam One September 27, 1999
Problem 6 (20points):
(a) (5 points) For the following expression derive a simplified sum of products expression using the given k-map.
F = ABC + AD + ABCD + BCD + ABC D
Simplified SOP F=________________________________________
(b) (15 points) Find the simplified product of sums (POS) expression for F in part (a).
Simplified POS ____________________________________________________________-
00 01 11 10
00
01
11
10
AB
CD
