ECE 462 HW4
1) Find a good variable ordering for
F = (a+be)(d+c)
Discuss your reasoning. Draw the Reduced Ordered BDD for your ordering.
[10 points]
2) For the following functions:
F = a+bc
G = bc+d
H = b+c+d
a) Draw BDDs F,G,H using variable ordering: a
deal less than we pay people who take care of our feet or our teeth. For
more descriptive statistics, consider Table 2. It shows the number of
unmarried men per 100 unmarried women in U.S. Metro Areas in 1990.
From this table we see that men outnumber wom
ECE 462 Logic Design
Midterm Exam II
12"h November, 2015
11:00 am - 12:20 pm
Name: E BIT/31L M41807 2 50h! .
Net ID: # 422 _.
0 This exam has 3 problems.
0 Write your name on every page
0 Show your work. Do not separate the pages of this booklet.
- You ar
ECE 462 Logic Design
Midterm Exam I
8th October, 2015
11:00 am - 12:20 pm
Name: SOLUTION
Net ID: SOLUTION
This exam has 4 problems. Make sure you have complete exam before you begin.
Write your name in every page in case pages become separated during
gr
Boolean Algebra
Boolean Algebra
Self-Taught: George Boole
Axiomatic Definition:
(more mathematical definition uses sets, relations, and lattices)
Huntingtons Postulates:
1. Closure: If a and b are elements of an algebra, then ab and a + b.
2. Zero Axiom
Another way to assess the models utility is to to test the hypothesis
H0 : 1 = 2 = = p = 0 versus H1 : at least one i , 0. The idea is that
if all is were zero, then the explanatory variables X1, . . . , Xp would be
worthless predictors for the response v
statistically significant and we conclude that the mean response differs
for trees with Tall = yes and trees with Tall = no. Remark 12.12. We were
somewhat disingenuous when we defined the dummy variable Tallyes
because, in truth, R defines Tallyes automa
parameters, which gives a difference of p j parameters (hence degrees
of freedom). The partial F statistic is F = (S S Er S S Ef)/(p j) S S Ef /(n
p 1) . (12.7.6) It can be shown when the regression assumptions
hold under H0 that the partial F statistic
2009. R package version 0.9-8. Available from: http:/CRAN.Rproject.org/package=mvtnorm. 180 [35] Rob Goedman, Gabor
Grothendieck, Sren Hjsgaard, and Ayal Pinkus. Ryacas: R interface to
the yacas computer algebra system, 2008. R package version 0.2-9.
Avai
Statistics: The Measurement of Uncertainty before 1900. Harvard
University Press, 1986. [82] Gilbert Strang. Linear Algebra and Its
Applications. Harcourt, 1988. 361 [83] Barbara G. Tabachnick and Linda
S. Fidell. Using Multivariate Statistics. Allyn and
package version 1.01. Available from: http:/CRAN.R-project.org/
package=DAAG. [65] Ben Mezrich. Bringing Down the House: The Inside
Story of Six M.I.T. Students Who Took Vegas for Millions. Free Press,
2003. 80 BIBLIOGRAPHY 393 [66] Jeff Miller. Earliest
FSMs
Prof. ShobhaVasudevan
ECE, UIUC
ECE 462
Definition
In mathematical terms, a (completely specified,
deterministic) Finite State Machine (FSM) of Mealy type is a
6-tuple
I, S,S0,O,
where:
I is the input alphabet i.e., a finite, non-empty set of input
K-Maps and the Quine-McCluskey
Method
Prof. Shobha Vasudevan
ECE, UIUC
ECE 462
Lecture 4
Quines Prime Implicant Theorem
A minimal sum must always consist of a sum
of prime implicants if a definition of cost is
used where an added literal will increase th
Introduction to Testing and
Design for Testability
Janak H. Patel
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
[email protected]
ECE 462
November 4, 2014
Outline
What is manufacturing Test?
Why test?
W
Dominance and the Branch and
Bound Method
Prof. Shobha Vasudevan
ECE, UIUC
ECE 462
Lecture 5
Row and Column Dominance
Row Equivalence row pi is equivalent to row pj if
pi and pj cover the same minterms in the prime
implicant chart
Rows pi and pj interse
Design for Test
Janak H. Patel
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
2013 Janak H. Patel
Outline
l What is Design for Test?
l Scan Based DFT
n LSSD
n Mux-based scan
2
What is Design for Testability?
1. Wiley, second edition, 1994. 143 392 BIBLIOGRAPHY [48] Norman L.
Johnson, Samuel Kotz, and N. Balakrishnan. Continuous Univariate
Distributions, volume 2. Wiley, second edition, 1995. 143 [49] Norman
L. Johnson, Samuel Kotz, and N. Balakrishnan. Discre
statistician and come to your own conclu- 387 sion. Detective Pyork E.
Pig *End File* 388 APPENDIX H. RCMDRTESTDRIVE STORY
Bibliography [1] Daniel Adler and Duncan Murdoch. rgl: 3D visualization
device system (OpenGL), 2009. R package version 0.87. Availa
does it mean? Consider the mean response (x1, x2) as a function of x2:
(x2) = (0 + 1 x1) + 2 x2. (12.5.3) This is a linear function of x2 with
slope 2. As x1 changes, the y-intercept of the mean response in x2
changes, but the slope remains the same. Ther
It is handled internally in a special way. Define a dummy variable
Tallyes that takes values Tallyes = 1, if Tall = yes, 0, otherwise.
(12.6.2) That is, Tallyes is an indicator variable which indicates when a
respective tree is tall. The model may now be
12.3. MODEL UTILITY AND INFERENCE 297 It turns out that there are
equally convenient formulas for the total sum of squares S S TO and the
regression sum of squares S S R. They are : S S TO =Y T I 1 n J ! Y
(12.3.2) and S S R =Y T H 1 n J ! Y. (12.3.3) (Th
distribution and compare it to the mean of the original sample: >
mean(xbarstar) [1] 3.056430 > mean(srs) [1] 3.05766 > mean(xbarstar) mean(srs) [1] -0.001229869 322 CHAPTER 13. RESAMPLING METHODS
Histogram of xbarstar xbarstar Density 2.4 2.6 2.8 3.0 3.2
they were previously. Notice that it was not necessary to rescale the
Girth prediction data before input to the predict function; the model
did the rescaling for us automatically. Remark 12.9. We have mentioned
on several occasions that it is important to
untreated 16 0.06 86 untreated 17 0.11 98 untreated 18 0.11 115
untreated D.5. EXPORTING DATA 359 D.5 Exporting Data The basic
function is write.table. The MASS package also has a write.matrix
function. D.6 Reshaping Data Aggregation Convert Tables to dat
log(Volume)~log(Girth)+ log(Height), and everything will proceed as
before, with one exception: we will need to be mindful when it comes
time to make predictions because the model will have been fit on the
log scale, and we will need to transform our pred
convention is to list the models from smallest to largest. 312 CHAPTER
12. MULTIPLE LINEAR REGRESSION > anova(treesreduced.lm,
treesfull.lm) Analysis of Variance Table Model 1: Volume ~ -1 + Girth +
I(Girth^2) Model 2: Volume ~ Girth + I(Girth^2) + Height
explanatory variables: a high R 2 indicates a strong dependence
between the selected independent variable and the others. The
redundant information inflates the variance of the parameter estimates
which can cause them to be statistically insignificant whe
freedom. (Remember, we are estimating p + 1 parameters.)
Consequently, under the null hypothesis H0 : i = 0 the statistic ti = bi/S
bi has a t(df = n p 1) distribution. 12.3.6 How to do it with R The
Students t tests for significance of the individual exp
At any time you can preview any released drafts with the development
version of the IPSUR package which is available from R-Forge: >
install.packages("IPSUR", repos = "http:/R-Forge.R-project.org") >
library(IPSUR) > read(IPSUR) 333 334 CHAPTER 14. CATEGO