AMCS 251 Numerical Linear Algebra -REPRISE
Professor: Alyn Rockwood
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Philosophy: Numerical Linear Algebra Where it fits
All problems Click to edit Master subtitle style
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Philosophy: Numerical Linear Algebr
CSCE 211:
Digital Logic Design
Chapter 6: Analysis of
Sequential Systems
Sequential System
A system that has memory
The output will depend not only on
the present input but also on the
past, on what has happened earlier
Will focus on clocked systems (also
CSCE 211:
Digital Logic Design
Chapter 5: Designing
Combinational Systems
Iterative System
A system implemented with
multiple copies of a smaller circuit
Consider 4-bit adder as an
example
10/03/2013
3
Delay in Combinational Logic
Circuits
When the input
CSCE 211:
Digital Logic Design
Chin-Tser Huang
huangct@cse.sc.edu
University of South Carolina
Chapter 2: Combinational
Systems
Objectives
Develop the tools to specify
combinational systems
Develop an algebraic approach for
the description, simplification
CSCE 211:
Digital Logic Design
Chapter 7: The Design of
Sequential Systems
Review: Design Process for
Combinational Systems
Step 1:
Represent each of the inputs and output in binary.
Step 1.5: If necessary, break the problem into smaller
subproblems.
Step
CSCE 211:
Digital Logic Design
Chapter 3: The Karnaugh
Map
Karnaugh Map (K-map)
The algebraic simplification method in
Ch. 2 is not systematical and does not
tell us whether the result is a minimum
We introduce the Karnaugh map, a
graphical approach to fi
CSCE 211:
Digital Logic Design
Chin-Tser Huang
huangct@cse.sc.edu
University of South Carolina
Chapter 1: Introduction
Digital Systems
They are everywhere!
They are usually binary: operating
on two-valued signals
Take an arbitrary number of inputs
and pro
CSCE 211: Digital Logic Design
Review Sheet for Midterm Test 2
Spring 2015
03/20/2015
This review sheet outlines the important topics from Chapter 3, Chapter 5 and Chapter 6.1 of the
textbook. It is meant as an informal study guide instead of a binding ag
Quiz 1 solution
50 minutes
All problems worth 10 points.
1. Convert the decimal number 311 to binary. Show your work.
311/2 = 155
rem 1
1
155/2 = 77
rem 1
11
77/2 = 38
rem 1
111
38/2 = 19
rem 0
0111
19/2 = 9
rem 1
10111
9 = 1001
100110111
2. Show the deci
Quiz 2 Solution
50 minutes
All problems worth 10 points.
Problems 1 to 3 require algebraic solurtions, NOT Karnaugh maps.
1. Reduce the following function to a sum of product expression with 3 terms
and 6 literals. Use algebra and show each step.
P9a
f =
Quiz 2
40 minutes
1. (15) For the following function,
f (x, y, z) = m (3, 4, 6, 7)
a)
b)
c)
d)
a)
Show a truth table.
Find a sum of products expression for f (not necessarily minimum).
Find a product of sums expression for f (not necessarily minimum).
Min
Gaussian Elimination
Algorithm to matrices: A = times 1st row subtract from second 3/2 times 1st row, subtract from third And so forth Click to edit Master subtitle style 2 0 0 2 -3 -2 3 -3/2 -7/2 2 1 3 2 -2 1 3 0 1
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Gaussian Elimination
Algorithm
Least Squares
General statement: For full rank A, m n, and m-vector b, find x such that | r | = | b Ax | is minimized We have x = A+b where A+ = (A*A)-1A* is called the generalized inverse Nearest point to b is y = Ax given by y = Pb Where the orthogonal
Conditioning and Stability
Conditioning: Small perturbation in input makes large change in function. Stability: Small perturbation in input makes a large change in the result of the method to compute the function
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Householder Triangularization Do you remember the projection
P = I aa*/a*a ?
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Householder Triangularization Do you remember the projection (Lecture 6)
P = I aa*/a*a ? Projects along a to orthogonal plane H H a Cl
AMCS 251
A mathematician is a blind man in a dark room looking for a black cat which isn't there. Charles Darwin
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Lecture 3 - Reprise
Induced norm What can you say about it?
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CSCE 211: Digital Logic Design
Spring 2015
Homework 4
03/05/15
This homework consists of 7 questions. Please find the corresponding questions from Section
5.10 in your textbook.
Follow this link to find Decoder and MUX instructions:
http:/www.cse.sc.edu/~