Chapter 1- Digital
Logic Circuits
Section 1.1 Digital Computers
What is the word digital mean?
The word digital implies information in computers is represented by variables that
take a limited number of discrete values.
(What is the opposite of digital?
2.171 Quiz 2 Solutions Problem 1: H(s) = a2 s 2 - a2
a) Calculate the zero order hold equivalent Heq (z). Heq (z) = z - 1 G(s) Zcfw_ z s
G(s) a2 Zcfw_ = Zcfw_ 2 s(s - a2 ) s G(s) A B
= Zcfw_ +
s(s + a) s(s - a) s
Zcfw_
Zcfw_
G(s) 1 a 1 a
= Zcfw_-
Problem Set 5 Solutions
library ieee; use ieee.std_logic_1164.all; use work.std_arith.all; - here is the declaration of entity entity la_rewarder is port (clk, go, SRAM_busy, SRAM_rdy: in std_logic; min: buffer std_logic_vector(2 downto 0); max: buffer st
Basics of MOS Large Signal Behavior (Qualitative)
Triode
VGS
ID
G
S
D
Cchannel = Cox(VGS-VT)
Pinch-off
VGS
ID
ID
G
S
Pinch-off
VD=V
D
Saturation
VGS
Overall I-V Characteristic
VDS=0
G
S
H.-S. Lee & M.H. Perrott
Triode
V
ID
Saturation
VDS
VD>V
D
MIT OCW
Ba
High Frequency, Broadband Amplifiers
The first thing that you typically do to the input signal
package
is amplify it
Connector
Adjoining pins
die
Controlled Impedance
PCB trace
Driving
Source
Z1
Vin
On-Chip
L1
Delay = x
Characteristic Impedance = Zo
Trans
8*n+16(%rbp)
16(%rbp)
%rdi, %rsi, %rdx,
%rcx, %r8 and %r9
%
% 8 d% 9
8(%rbp)
0(%rbp)
-8(%rbp)
%rbp
'
marks the beginning
of the current frame
-8*m-8(%rbp)
0(%rsp)
argument n
argument 7
Return address
Previous %rbp
local 0
local m
Cu
urrent
Arguments 0
6.033 Spring 2008, Quiz 2
Page 2 of 11
I Reading Questions
1. [6 points]: Which of the following statements are true of Ethernet (as described in the Ethernet
paper, reading #9)?
(Circle True or False for each choice.)
A. True / False Ethernet enforces a
Homework 3
1. In our previous lectures we studied complexity classes P
and NP, as well as NP-complete problems. The relations
between those classes are shown in the following diagram:
Are there any problems that belong to the class NP, but
lay outside bot
Introduction to Algorithms
Massachusetts Institute of Technology
Professors Erik Demaine and Shafi Goldwasser
May 7, 2004
6.046J/18.410J
Handout 25
Problem Set 7 Solutions
This problem set is due in recitation on Friday, May 7.
Reading: Chapter 22, 24, 25
Discrete Math for Bioinformatics WS 11/12, by A. Bockmayr/K. Reinert, 13. Februar 2012, 16:03
9009
Reducing 3SAT to INDEPENDENT SET
Let F be a conjunction of n clauses of length 3, i.e., a disjunction of 3 propositional variables or their
negation.
Cons
Greedy Algorithm (17.4/16.4)
Greedy Algorithm (GA)
always makes choice which is the best at the moment
does not look ahead: local
very powerful in practice: simplest and fastest
in general, does not return the optimal solution
Example: convex polygon mi
Single-Source Shortest Paths (25/24)
HW: 25-2 and 25-3 p. 546/24-2 and 24-3 p.615
Given a graph G=(V,E) and w: E
weight of <v[1],.,v[k]> is w(p) = w(v[i],v[i+1])
Single-source shortest-paths:
find a shortest path from a source s to every
vertex v V
Sing
The Issue of Velocity Saturation
We often assume that MOS current is a quadratic
function of Vgs:
It can be shown, more generally
-V
corresponds to the saturation voltage at a given
length, which we often refer to as V
dsat,l
- In strong inversion below v
Reflection Coefficient
We defined, at the load
Load and characteristic impedances were related
Alternately
Can we find reflection coefficient at locations other than
the load location?: Generalized reflection coefficient
H.-S. Lee & M.H. Perrott
MIT OCW
V
6.826Principles of Computer Systems
2002
6.826Principles of Computer Systems
APROC Begin() = < Abort(); ph := run >
27. Distributed Transactions
In this handout we study the problem of doing a transaction (that is, an atomic action) that
involves actions
Chap. 1-4 Map
Simpification
Goal: To obtain the simplest implementation for a given
function
Introduce a graphical technique using Karnaugh maps (K-maps for
short)
Karnaugh Map (K-map)
A K-map is a collection of squares
Each square represents a minterm
Cha1-2 Logic Gates
Binary variables take on one of two values.
Logical operators operate on binary values and binary
variables.
Basic logical operators are the logic functions AND, OR
and NOT.
Logic gates implement logic functions.
Logical Operations
Chap 1-3 Boolean
Algebra
Boolean Algebra: a useful mathematical system
for specifying and transforming logic functions.
We study Boolean algebra as a foundation for
designing and analyzing digital systems!
Boolean Algebra
Invented by George Boole in 185
Greedy Algorithm (17.4/16.4)
Greedy Algorithm (GA)
always makes choice which is the best at the moment
does not look ahead: local
very powerful in practice: simplest and fastest
in general, does not return the optimal solution
Example: convex polygon mi
Technology futures
Communications
Input/Output
Computing
Communications
Bandwidth will get much, much cheaper and more
available.
More people will have more decision-making power in
organizations.
Will videoconferencing be as good as being there?
W
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.111 - Introductory Digital Systems Laboratory
Problem Set 1 Solutions
Issued: February 8, 2006
Boolean Algebra Practice Problems (not graded)
1)
2)
3)
4)
5)
Three generations of the Web
1st generation (early 1990s)
You see static web pages
Needed: URL, HTTP, HTML
2nd generation (late 1990s)
Simple interactions between humans and remote applications
E.g., You fill out a form on a web page to order a prod
Some of the figures in this lecture are courtesy of Alex Allister Shvartsman. Used with permission.
6.826Principles of Computer Systems
2002
6.826Principles of Computer Systems
Medium
Alpha EV7
chip
PC board
23. Networks Links and Switches1
Links
A link i
6.826Principles of Computer Systems
2002
6.826Principles of Computer Systems
2002
Efficiency. If we anticipate lots of references to objects, we will be concerned about
efficiency. There are various tricks that we can use to make things run faster:
24.
Major IT applications in business
Executive
Support
Systems
5year
sales
trend
forecasts
5year
operating
plan
Sales
Inventory Annual
management control
budgeting
Management
Information
Systems
Salesregion
analysis
Knowledge
Worker
Systems
Engineering
works
6.826Principles of Computer Systems
2002
2002
if there are n components and each fails independently with small probability pc, then the system
fails with probability n pc. As n grows, this number grows too. Furthermore, it is often expensive
to make high
A+C
ab
ab
00
c
0
1
01
11
10
0
X
X
1
0
1
1
X
1
1
00
c
This is MPS
1
10
0
X
X
1
1
01
11
10
X
1
C
0
X
X
1
0
1
1
X
1
1
00
c
A
1
ab
00
0
11
This is MSP
ab
c
01
01
11
10
0
X
X
1
1
1
X
1
Q Q
2
Q x
0
00
Q Q
1
2
01
11
10
00
0
0
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0
01
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Dynamic Sets (III, Introduction)
Dynamic sets (Data structures):
we change a dictionary, add/remove words
reuse of structured information
on-line algorithms - very fast updating
Elements:
record
x key
sat-te
data
key field is the element ID, dynamic
Master Method (4. 3)
Recurrent formula T(n) = a T(n/b) + f(n)
logb a
f
(
n
)
O
(
n
) for some > 0 then
1) if
T (n) (n logb a )
log b a
f
(
n
)
(
n
)
2) if
log
3) if f (n) (n
b
a
log b a
T
(
n
)
(
n
log n)
then
)
for some > 0
a f(n/b) c f(n) for some c <