BOOLEAN ALGEBRA AND LOGIC
SIMPLIFICATION
Chapter 04
History / Introduction
In 1854, George Boole
Logical Algebra Now Boolean Algebra
In 1938, Claude Shannon
Boolean algebra is the mathematics of Digital
Systems
AND, OR, NOT, NAND and NOR gates perform
si
Number Systems, Operations
and Codes
Chapter 02
Decimal Number System
The decimal number system has ten unique digits 0, 1,
2, 3 9. Using these single digits, ten different values
can be represented.
The decimal number system is a positional number
syst
Logic Gate
Chapter 03
Logic Gates
Basic building blocks of a digital system.
Identification of Logic gates (Symbols ):
AND Gate
F=A.B
AND Gate
Timing diagram
AND Gate
Example
Enable / Disable device
Counter counts when it receive pulses.
OR Gate
F
Introductory Concepts
Chapter 01
Topics
Digital and analog quantities
Binary Digits
Logic Levels & waveforms
Basic logic operations
Overview of basic logic functions
Digital and analog quantities
Analog Quantity:
Continuous values
Intensity of lig
Combinational Logic Analysis
Chapter 05
Combinational Logic
When logic gates are connected together to
produce a specified output for certain
specified combination of input variables, with
no storage involved, the resulting circuit is in
the category of
Introductory Concepts
Chapter 01
Topics
Digital and analog quantities
Binary Digits
Logic Levels & waveforms
Basic logic operations
Overview of basic logic functions
Digital and analog quantities
Analog Quantity:
Continuous values
Intensity of lig
Latches and FlipFlops
Chapter 07
Sequential Digital Circuits
Sequential circuits are digital circuits in which the outputs
depend not only on the current inputs, but also on the
previous state of the output.
The basic sequential circuit elements can be
BOOLEAN ALGEBRA AND LOGIC
SIMPLIFICATION
Chapter 04
History / Introduction
In 1854, George Boole
Logical Algebra Now Boolean Algebra
In 1938, Claude Shannon
Boolean algebra is the mathematics of Digital
Systems
AND, OR, NOT, NAND and NOR gates perform
si
Laws and Theorems of Boolean Algebra:
Operations with 0 and 1:
1. X + 0 = X
2. X + 1 = 1
1D. X 1 = X
2D. X 0 = 0
Idempotent laws:
3. X + X = X
3D. X X = X
Involution law:
4. (X')' = X
Laws of complementarity:
5. X + X' = 1
5D. X X' = 0
Commutative laws:
6
Introduction to Electrical and Computer Engineering
ELECTRICAL 110

Winter 2014
ECE110 Haken Lecture 11
Learning objectives
Analyze power sourcing/sinking from IV curves
Find (V,I) operating points of connected subcircuits
Recognize the connection between IV curves and Thvenin
and Norton equivalent circuits
Hour Exam #1is on Mond
Introduction to Electrical and Computer Engineering
ELECTRICAL 110

Winter 2014
Lecture 16 ECE110 Haken
Learning objectives
° Be able to solve Circuit Analysis problems
involving sources, resistances, and diodes.
 Prove the functionality of diodebearing circuits
such as the halfwave rectier, the fullwave
rectier, and the diod
ECE 110 Laboratory AB9
Jong Hyun Lee
Hyun Bin Kim
26th April 2012
Final Car Report
Introduction
With all the facts and knowledge that we have learned so far in ECE lab, the final lab
is to build a car with given sensors, make a coding since this lab's car
ECE 110
Professor Frizzell
4 April 2012
Wireless technology
It is said that technology is always changing, but what is technology? In short, technology
is anything that we use to advance the ease of accomplishing tasks. Technology is mostly seen
as an ele
ECE 110 Laboratory AB9
Jong Hyun Lee
Hyun Bin Kim
26th April 2012
Final Car Report
Introduction
With all the facts and knowledge that we have learned so far in ECE lab, the final lab
is to build a car with given sensors, make a coding since this lab's car
Page 1
This page is to be completed by the author of the draft paragraph.
Draft Paper Assessment for JongHyun Lee
Date (before rotation): 3/30/12
Date (after rotation): 4/1/12
Write personal comments (how much did you benefit from this exercise, etc) afte
1
ECE 534: Elements of Information Theory
Midterm Exam I (Spring 2007) Problem 1 [20 pts] What are the relations (, =, ) between the following pairs of expressions? Explain why. 1) H (5X ) and H (X ); 2) H (X0 X1 ) and H (X0 X1 , X1 ); 3) H (X1 , X2 , .
1
ECE 534: Elements of Information Theory Solutions to Midterm Exam (Spring 2006)
Problem 1 [20 pts.] A discrete memoryless source has an alphabet of three letters, xi , i = 1, 2, 3, with probabilities 0.4, 0.4, and 0.2, respectively. (a) Find the binary