**LOGIC DESIGN OF SWITCHING CIRCUITS**

** INTRODUCTION**

This video presents the contents of the 18 chapters of the Course Logic Design of Switching Circuits based in the book with the same name. This book is a text book for Electrical and Electronics Engineering and Technology Courses

**LOGIC DESIGN OF SWITCHING CIRCUITS**

** CHAPTER 1 PART 1**

Counting Systems

Number Bases

Decimal Base (10)

Binary Base (2)

Octal Base (8)

Hexadecimal Base (16)

Bit, Byte, Nibble, Word

**LOGIC DESIGN OF SWITCHING CIRCUITS**

** CHAPTER 1 PART 2**

Definition of Numerical Base

Conversion from Any Base to Base 10

Conversion from Base 10 to Any Base

Union of Integer and Fractional Part of Converted Number

**LOGIC DESIGN OF SWITCHING CIRCUITS**

** CHAPTER 1 PART 3**

Equivalence between Bases

Binary and Octal

Binary and Hexadecimal

Octal and Binary

Hexadecimal and Binary

Definition of Logic – Physical and Logical Level

https://www.youtube.com/watch?v=vrCsO9pq3wU

**LOGIC DESIGN OF SWITCHING CIRCUITS**

** CHAPTER 1 PART 4**

Codification Systems:

BCD

Excess 3 Code

Gray Code

ASCII Tables

(American Standard Code for Information Interchange)

**LOGIC DESIGN OF SWITCHING CIRCUITS**

** CHAPTER 1 PART 5**

Codes Conversion

Decimal do Gray Code

Gray Code to Decimal

**LOGIC DESIGN OF SWITCHING CIRCUITS**

** CHAPTER 1 PART 6**

Operations using Binary Numbers

Sum Operation

Subtraction Operation

Conversion Binary Positive to Binary Negative

Conversion Binary Negative to Binary Positive

**LOGIC DESIGN OF SWITCHING CIRCUITS**

** CHAPTER 1 PART 7**

Solved Problems

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 1**

Combinational Switching Circuits

Definition of Combinacional Switching Circuits

Adder Complete Circuit

Subtractor Complete Circuit

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 2**

Input Symbol of a Combinational Circuit

Input Alphabet of a Combinational Circuit

Output Symbol of a Combinational Circuit

Output Alphabet of a Combinational Circuit

Mapping or True Table

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 3**

Algebraic Operations

DUO Operation

TRI Operation

Commutative Property of Operations

Associative Property of Operations

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 4**

Boolean Algebra Operations

Unary Operations of Boolean Algebra

Boolean Operations with two Inputs

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 5**

Definitions of Boolean Algebra

Definitions of Digital Boolean Algebra

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 6**

Boolean Forms

Equivalence of Boolean Forms

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 7**

Theorems of Boolean Algebra

Theorem 1

Theorem 2

Theorem 3

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 8**

Theorems of Boolean Algebra

Theorem 4

Theorem 5

Theorem 6

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 9**

Theorems of Boolean Algebra

Theorem 7

Theorem 8

Theorem 9

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 10**

Theorems of Boolean Algebra

Theorem 10 – De Morgan

Theorem 11 – De Morgan – Extension

Theorem12 – Associativity Property of Operations AND and OR

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 11**

Operation XOR

Operation XNOR

**LOGIC DESIGN OF SWITCHING CIRCUITS**

**CHAPTER 2 PART 12**

Solved Problems

Problem 1

Problem 2

**BASIC GEOMETRY – INTRODUCTION**

Presentation of the Contents of Each of the Chapters of the Course of Basic Geometry

Introduction

Chapter 1 – Basic Elements of Plane Geometry

Chapter 2 – Postulates of Plane Geometry

Chapter 3 – This Chapter shows the Definitions, Properties and Construction of the Triangles:

Chapter 4 – This Chapter Show the Definitions, Properties, and Construction of Quadrilaterals

Chapter 5 – This Chapter Show the Definitions, Properties, and Construction of Circumferences, Circles, and their Elements

Chapter 6 – This Chapter Shows the Definitions, Properties, and Construction of Various Types of Regular Polygons

Chapter 7 – This Chapter Shows the Definitions, Properties, and Construction of Ellipse, Hyperbola, and Parable Conic Curves

**BASIC GEOMETRY**

**CHAPTER 1 – PART 1**

Representation of Points, Lines and Plans

Symbols of Relations

Relations between Points, Lines and Plans

Definitions of Basic Elements of Lines and Plans

Definitions of Basic Elements of Circumference and Circle

**BASIC GEOMETRY**

**CHAPTER 1 PART 2**

Definitions of Angle and Types of Angles

Definitions of Complementary and Supplementary Angles

Definitions of Acute, Right, and Obtuse Angles

Definitions of bisector of an angle and bisector of a line

Equivalence of Angle Measurements

**BASIC GEOMETRY**

**CHAPTER 2 – PART 1**

Definitions Related to Points, Lines and Plans

Definitions of a Plane by Three-Point

Relations between Points with Lines and Plans

Definition of Semi Plane

Congruent Lines

Definitions of Concurrent and Parallel Lines

Perpendicular Lines

**BASIC GEOMETRY**

**CHAPTER 2 – PART 2**

Euclid’s Postulate for no Parallel Straight Lines

Euclid’s Postulate of Parallelism

Theorem on Definition of Plane by Line and Point

Theorem on Definition of Plane by Concurrent Straight Lines

Theorem on Definition of Plane by Parallel Lines

Method for Division of a Segment of Line in Sub Segments with same dimension

Proportionality of Line Sub Segments between Parallel Lines

**BASIC GEOMETRY**

**CHAPTER 3 – PART 1**

Basic Triangle Definitions

Definition of Triangle Perimeter

Equilateral Triangle definition

Building a Triangle Equilateral

Isosceles triangle definition

Definition of a Scalene Triangle

Definitions of Triangle Types based on angle values

Rectangle Triangle Definition

Similar Triangles

**BASIC GEOMETRY**

**CHAPTER 3 – PART 2**

Sum of the three Interior Angles of a Triangle

Conditions for Congruence of Triangles

Construction of Triangle given One Side and Two Angles

Definition of Exterior Angles of a Triangle

Relations between Interior and Exterior angles of a Triangle

**BASIC GEOMETRY**

**CHAPTER 3 – PART 3**

Definitions of Height and Orthocenter of a Triangle

Definition of Circumcenter of a Triangle and of a Circumference Exterior Circumscribed to a Triangle

Definition of a Centroid and Median of a Triangle

Relations between Median segments and Centroid

Relations between dimensions of the Hypotenuse and dimensions of the Median, in a Rectangle Triangle

**BASIC GEOMETRY**

**CHAPTER 3 – PART 4**

Concept of the bisector of an angle and Inscribed Circumference

Definition of Incenter of a Triangle

Calculation of the Area of an Acute Triangle

Calculation of the Area for a Right Triangle

Calculation of the Area of a Obtuse Triangle

**BASIC GEOMETRY**

**CHAPTER 3 – PART 5**

Theorem of Equivalence of the Areas of Parallelograms and Triangles between Parallel Lines

Theorem of Pythagoras of Samos, that proves the relation between the Hypotenuse and the Catheti or legs in a Rectangle Triangle.

**BASIC GEOMETRY**

**CHAPTER 4 – PART 1**

Definition of Quadrilaterals

Quadrilaterals Convex and Concave

Perimeter of a Quadrilateral

Sum of the Interior Angles of Quadrilaterals

Sum of Exterior Angles of Quadrilaterals

Definition of a Square Quadrilateral

Calculation of Area of a Square Quadrilateral

Definition of Inscribed and Circumscribed Circumferences of a Square Quadrilateral

Definition of a Rectangle Quadrilateral

Area of a Rectangular Quadrilateral

**BASIC GEOMETRY**

**CHAPTER 4 PART 2**

Definition of Parallelograms

Area of a Quadrilateral Parallelogram

Definition of a Rhomboid Parallelogram

Area of a Rhomboid Parallelogram

Definition of the Scalene Trapezoid Quadrilateral

Definition of Isosceles Trapezoid Quadrilateral

**BASIC GEOMETRY**

**CHAPTER 4 – PART 3**

Area of Quadrilateral Trapezoid

Theorem of Equivalence of the Areas of a Triangle and a Parallelogram Constructed between Parallel Lines using the Same Base

Definition and Properties of the Golden Segment and Golden Rectangle

Definition of Golden Ratio or Golden Number

Construction of Golden Segment and Golden Rectangle

**BASIC GEOMETRY**

**CHAPTER 5 –PART1**

Basic Definitions of Circumference and Circles

Radio and Diameter Definitions

Definitions on Half Circumference and Semicircle

Definitions of Internal and External Points to a Circumference

Perimeter of a Circle or Length of a Circumference

Area of a Circle

Circle Sector or Circular Sector

Definitions of Arc, Circular Segment, Sagitta and Chord

Circular Segment of One Chord

Circular Segment of two Chords

Definitions of Circular Crown

Definition of Circular Crown Sector

**BASIC GEOMETRY**

**CHAPTER 5 – PART 2**

Relative Positions of Two Circumferences Secants

Relative Positions of Two Circumferences Tangents

Relative Positions of Two Circumferences no Tangents and no Secants

Positions of Straight Lines Tangents to the Circumference

Positions of Straight Lines regarding a Circumference or Circle

Properties of Straight Lines Secants to the Circumference

Tangent Segments

Chords Equidistant in a Circumference or Circle

**BASIC GEOMETRY**

**CHAPTER 5 – PART 3**

Circumference Inscribed in a Triangle

Circumference Inscribed in a Quadrilateral

Circumscribed Circumference of a Triangle

Circumference Circumscribed in a Quadrilateral

Arc Minor and Arc Major

Inscribed Angle

Right Angle

Tangent Chord Angle

**BASIC GEOMETRY**

**CHAPTER 5 – PART 4**

Arc Capable

Power of a Point P internal to a Circumference

Power of a Point P External to a Circumference

Power of a Point P External to a Circumference with a Tangent Line

Fibonacci Spiral and Logarithmic Spiral

**BASIC GEOMETRY**

**CHAPTER 6 – PART 1**

Definitions of Polygons Concave and Convex

Definitions of Polygons Regular and no Regular

Types of Regular Polygons

Important Entities and Structures of Regular Polygons

**BASIC GEOMETRY**

**CHAPTER 6 – PART 2**

Formulas of Relationships between Elements of Circumscribed Circumference and the Side Triangle

Table of Values for the Central Angle, Sine and Cosine

Calculation of the value of the side, apothem and area of the side triangle

Sum of the External Angles of a Polygon

Sum of Internal Angles of a Polygon

Number of Diagonals of a Polygon

Values of angles in a Regular Polygon

**BASIC GEOMETRY**

**CHAPTER 6 – PART 3**

Polygon Regular Hexagon

Polygon Regular Triangle

Polygon Regular Dodecagon

Polygon Regular Square

Polygon Regular Octagon

**BASIC GEOMETRY**

**CHAPTER 6 – PART 4**

Polygon Regular Decagon

Polygon Regular Pentagon

Polygon Regular Heptagon

**BASIC GEOMETRY**

**CHAPTER 6 – PART 5**

Polygon Regular Nonagon

Polygon Regular Undecagon

Final Considerations on Regular Polygons

Problems to be solved

**BASIC GEOMETRY**

**CHAPTER 7 – PART 1**

Definitions about Ellipse Curve

Eccentricity de la Ellipse

Construction of am Ellipse

Tangent to point of an Ellipse

Inner and Outer Concentric Circles

Length Latus Rectum (LR)

Circles Director of Ellipse

Other Definitions for the Ellipse

**BASIC GEOMETRY**

**CHAPTER 7 – PART 2**

Definitions about the Hyperbola Curve

Eccentricity of Hyperbola

https://www.youtube.com/watch?v=1Bl-d6gqKAc

**BASIC GEOMETRY**

**CHAPTER 7 – PART 3**

Construction of Hyperbola

Tangent to a point of Hyperbola

Auxiliary Circle of Hyperbola

Director Circles of Hyperbola

Asymptotes of a Hyperbola

Other Definitions for Hyperbola

**BASIC GEOMETRY**

**CHAPTER 7 – PART 4**

Definitions of the Parabola Curve

Construction of the Parabola

Tangent to the Curve of Parabola

Other Definitions about the Parabola Curve

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