Lab 7: Introduction to
Behavioral Verilog and Logic
Synthesis
Josh McGuire
ECEN 248-505
TA: Yuhan Zhou
10-20-14
OBJECTIVES:
The objective of this lab is to learn a higher level of abstraction that is called behavioral Verilog
and this is used to improve t

ECEN 303: Random Signals and Systems
Spring 2010 Final Exam Guidelines
1. Final exam dates: Section 501: 3:00 5:00 PM Friday May 7, ZAC 223C Section 502: 1:00 3:00 PM Monday May 10, ZAC 223C The exams are closed-book and closed-notes. However, you are all

ELEN 303: Assignment 1
Instructor: Email: Oce: Oce Hours: Dr. Jean-Franois Chamberland c chmbrlnd@ece.tamu.edu (Subject ECEN 303) Room 244F WERC Tue 2:30 - 3:45 p.m.
Problems: 1. Following the argument presented in the notes, prove that
c
S
A c
=

ECEN 303: Random Signals and Systems Fall 2009
Instructor: Dr. Jean-Francois Chamberland Assistant Professor Department of Electrical and Computer Engineering Room 244F, WERC chmbrlnd@ece.tamu.edu (Subject: ECEN 303) (979) 845-6204 http:/www.ece.tamu.edu/

ECEN 303: Assignment 8
Problems: 1. If X is a random variable that is uniformly distributed between 1 and 1, fnd the PDF of |X | and the PDF of ln |X |. Let Y = |X |. We have, for 0 y 1, FY (y ) = Pr(Y y ) = Pr and therefore by dierentiation, fY (y ) = 2y

ECEN 303: Assignment 7
Problems: 1. Let X have the PDF |x| e , 2 satises the normalization condition, and evaluate
fX (x) = where is a positive scalar. Verify that fX the mean and variance of X . Consider the integral
|x| e dx = 2
0
x e dx + 2
0
x

ECEN 303: Assignment 4
Problems: 1. De Mrs puzzle. A six-sided die is rolled three times independently. Which is more likely: ee a sum of 11 or a sum of 12? (This question was posed by the French nobleman de Mr to ee his friend Pascal in the 17th century.

ECEN 303: Assignment 3
Problems: 1. Fifty-two percent of the students at a certain college are females. Five percent of the students in this college are majoring in computer science. Two percent of the students are women majoring in computer science. If a

ECEN 303: Assignment 6
Problems: 1. Two fair dice are rolled. Find the joint probability mass function of X and Y when (a) X is the largest value obtained on any die and Y is the sum of the values; In this rst case, we have pX,Y (x, y ) 1 2 3 4 5 6 2
1 36

Math 311-503
Spring 2007
Sample problems for Test 1: Solutions
Any problem may be altered or replaced by a dierent one!
Problem 1 (25 pts.)
Let be the plane in R3 passing through the points (2, 0, 0),
(1, 1, 0), and (3, 0, 2). Let be the line in R3 passin

Math 311-503
March 29, 2007
Test 2: Solutions
Problem 1 (20 pts.)
Determine which of the following subsets of R3 are subspaces.
Briey explain.
(i) The set S1 of vectors (x, y, z) R3 such that xyz = 0.
(ii) The set S2 of vectors (x, y, z) R3 such that x +

Math 311-503
February 13, 2007
Test 1: Solutions
Problem 1 (30 pts.) Let be the plane in R3 passing through the points (1, 0, 0), (0, 0, 1),
and (0, 1, 2). Let be the line in R3 passing through the points (1, 0, 1) and (2, 0, 2).
(i) Find a parametric rep

Math 311-503
February 13, 2007
Test 1
Problem 1 (30 pts.) Let be the plane in R3 passing through the points (1, 0, 0), (0, 0, 1),
and (0, 1, 2). Let be the line in R3 passing through the points (1, 0, 1) and (2, 0, 2).
(i) Find a parametric representation

Math 311-503
May 9, 2007
Final exam: Solutions
Problem 1 (25 pts.)
and p(3) = p(1).
Find a quadratic polynomial p(x) such that p(1) = 2, p(2) = 3,
Solution: p(x) = x2 2x + 3.
A quadratic polynomial p(x) = ax2 + bx + c is the desired one if its coecients s

Math 311-503
Spring 2007
Sample problems for the nal exam
Any problem may be altered or replaced by a dierent one!
Problem 1 (20 pts.) The planes x + 2y + 2z = 1 and 4x + 7y + 4z = 5 intersect in a
line. Find a parametric representation for the line.
Prob

Math 311-503
Spring 2007
Sample problems for Test 1
Any problem may be altered or replaced by a dierent one!
Problem 1 (25 pts.)
Let be the plane in R3 passing through the points (2, 0, 0),
(1, 1, 0), and (3, 0, 2). Let be the line in R3 passing through t

Math 311-503
Spring 2007
Sample problems for Test 2
Any problem may be altered or replaced by a dierent one!
Problem 1 (20 pts.) Let P2 be the vector space of all polynomials (with real coecients)
of degree at most 2. Determine which of the following subs

Math 311-503
May 9, 2007
Final exam
Problem 1 (25 pts.)
and p(3) = p(1).
Find a quadratic polynomial p(x) such that p(1) = 2, p(2) = 3,
Problem 2 (30 pts.) Consider a linear operator L : R3 R3 given by
L(v) = v v0 ,
where v0 = (1, 1, 1).
(i) Find the matr

Math 311-503
March 29, 2007
Test 2
Problem 1 (20 pts.)
Determine which of the following subsets of R3 are subspaces.
Briey explain.
(i) The set S1 of vectors (x, y, z) R3 such that xyz = 0.
(ii) The set S2 of vectors (x, y, z) R3 such that x + y + z = 0.

Assignment 7
1. Consider four independent rolls of a 6-sided die. Let X be the number of 1s and let Y be
the number of 2s obtained. What is the joint PMF of X and Y ?
Solution: The joint PMF of X and Y is given by
pX,Y (i, j) =
4
i,j,4ij
1 i+j
6
4 4ij
6
,

1
To directly cacluate
n
k=1 k
( )
n
= n2n1 in P. 5 (b) of Assignment 1.
k
n
(n)
n(n 1)
n(n 1)(n 2)
k
=n+2
+3
+ + n
k
2!
3!
k=1
(
)
(n 1)(n 2)
= n 1 + (n 1) +
+ + 1
2!
n1 (
n 1)
.
=n
l
(1)
l=0
According to binomial theorem, i.e.,
n
(1 + x) =
n
(n)
l=0

MATH 311
Topics in Applied Mathematics I
Lecture 14:
Review for Test 1.
Topics for Test 1
Part I: Elementary linear algebra (Leon/Colley
1.11.5, 2.12.2)
Systems of linear equations: elementary
operations, Gaussian elimination, back substitution.
Matrix

MATH 311503/505
Fall 2015
Sample problems for the nal exam
Any problem may be altered or replaced by a dierent one!
Problem 1 Find the point of intersection of the planes x + 2y z = 1, x 3y = 5, and
2x + y + z = 0 in R3 .
Problem 2 Consider a linear opera

MATH 311
Topics in Applied Mathematics I
Lecture 38:
Review for the nal exam.
Topics for the nal exam: Part I
Elementary linear algebra (L/C 1.11.5, 2.12.2)
Systems of linear equations: elementary
operations, Gaussian elimination, back substitution.
Mat

MATH 311
Topics in Applied Mathematics I
Lecture 37:
Review for Test 3.
Topics for Test 3
Vector analysis (Leon/Colley 8.18.4, 9.19.5, 10.110.3,
11.111.3)
Gradient, divergence, and curl
Fubinis Theorem
Change of coordinates in a multiple integral
Lengt

MATH 311
Topics in Applied Mathematics I
Lecture 39:
Integration of dierential forms.
Review for the nal exam (continued).
Vector line and surface integrals
Any vector integral along a curve Rn can be
represented asa scalar lineintegral:
F ds =
(F t) ds,

MATH 311
Topics in Applied Mathematics I
Lecture 27:
Review for Test 2.
Topics for Test 2
Vector spaces (Leon/Colley 3.43.6)
Basis and dimension
Rank and nullity of a matrix
Coordinates relative to a basis
Change of basis, transition matrix
Linear tra

MATH 311503/505
Fall 2015
Sample problems for the nal exam: Some solutions
Any problem may be altered or replaced by a dierent one!
Problem 1 Find the point of intersection of the planes x + 2y z = 1, x 3y = 5, and
2x + y + z = 0 in R3 .
The intersection

Math 311-503
Spring 2007
Sample problems for the nal exam: Solutions
Any problem may be altered or replaced by a dierent one!
Problem 1 (20 pts.) The planes x + 2y + 2z = 1 and 4x + 7y + 4z = 5 intersect in a
line. Find a parametric representation for the

Math 311-503
Spring 2007
Sample problems for Test 2: Solutions
Any problem may be altered or replaced by a dierent one!
Problem 1 (20 pts.) Let P2 be the vector space of all polynomials (with real coecients)
of degree at most 2. Determine which of the fol

ECEN 303: Random Signals and Systems
Fall 2016
Midterm II exam
Problem 1(30pts): Before going out, John checks the weather report to decide whether bring an
umbrella or not. If the forecast is rain, the probability of actually raining that day is 80%; if

ECEN 303: Random Signals and Systems
Fall 2016
Midterm I exam
Problem 1: A box contains 4 red and 7 blue balls.
a. How many ways can we arrange all of them in one line if only all the red balls must be
together?
b. How many ways can we draw 3 red and 4 bl

ECEN 303: Random Signals and Systems
Fall 2015
Practice final exam
1. A software company, called Aggdroid, develops products for Android smart phones. Aggdroid
creates applications using Assembly, C and Java. There are 30 employees at Aggdroid who
can pro

CSCE 206 | Exam 3 | Fall 2015 | Solution
B
1. B
2. B
3. A
4. A
5. B
6. B
7. A
8. B
9. B
10. A
11. A
12. B
A
13. AB
14. B
15. A
16. C
17. D
18. B
19. C
20. D
21. D
22. A
23. B
24. C
25. B
26. D
27. D
28. D
29. C
30. D
31. B
32. D
33. C
34. E
35. C
36. A
37

CSCE 206 | Exam 3 | Fall 2015 | Solution
A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
B
B
B
A
A
B
A
B
B
B
A
A
A
B
A
D
D
A
B
C
C
D
B
C
B
D
D
B
D
D
C
D
C
C
E
E
37.
3