Basic Electronics Math (eBook)

Front Cover 1
Basic Electronics Math 4
Copyright Page 5
Table of Contents 6
Chapter 1. Arithmetic Fractions 14
1.1 Introduction 14
1.2 Rounding Off Numbers 14
1.3 Common Fractions 15
1.4 Addition of Fractions 15
1.5 Subtraction of Fractions 16
1.6 Mixed Numbers 16
1.7 Mathematical Expressions and Terms 17
1.8 Signs of Grouping 17
Summary 18
Chapter 2. Operations with Powers and Roots of Numbers 19
2.1 Introduction 19
2.2 Extraction of Square Roots 20
2.3 Roots of Fractions 21
2.4 Powers and Roots 21
2.5 Higher Powers and Roots of Numbers 22
Summary 23
Chapter 3. Scientific Notation and Powers of Ten 24
3.1 Scientific Notation (Powers of Ten) 24
3.2 Signs of Exponents 24
3.3 Addition and Subtraction of Powers of Ten 25
3.4 Multiplying with Powers of Ten 26
3.5 Dividing by Powers of Ten 26
3.6 Multiplication and Division Combined 27
3.7 Laws of Exponents 28
3.8 Raising a Power of Ten to a Power 28
3.9 Taking the Root of a Power of Ten 28
Summary 29
Chapter 4. Units--Measurements and the Metric System 31
4.1 Introduction 31
4.2 Units for Electronics 31
4.3 Ranges of Electrical Units 32
4.4 Systems of Measurement 33
4.5 The English System of Measurement 33
4.6 The SI Metric System of Measurement 33
4.7 A Summary of the Most Commonly Used Metric Measurements 34
4.8 Relationships Between the Metric and the English Systems 35
4.9 The Micron and the Mil 36
4.10 Style and Usage of the International System of Units (SI) 36
Summary 38
Chapter 5. Computer Numbering Systems 39
5.1 Introduction 39
5.2 Decimal Numbering System (Base 10) 39
5.3 Binary Numbering System (Base 2) 40
5.4 Binary to Decimal Conversion 40
5.5 Decimal to Binary Conversion 40
5.6 Octal Numbering System (Base 8) 41
5.7 Converting Binary Numbers into Octal Numbers 41
5.8 Hexadecimal Numbering System (Base 16) 42
5.9 Addition of Binary Numbers 42
5.10 Addition of Octal Numbers 44
5.11 Additional of Hexadecimal Numbers 44
5.12 Subtraction of Binary Numbers 44
5.13 Two's Complement 46
5.14 Eight's and Sixteen's Complement 47
5.15 Subtracting Octal Numbers 47
Summary 48
Chapter 6. Introduction to Algebra 49
6.1 Introduction 49
6.2 Expressed and Implied Signs of Algebraic Operations 49
6.3 Numerical and Literal Algebraic Expressions, Equations, and Formulas 50
6.4 Terms in Algebraic Expressions, Equations, and Formulas 51
6.5 Similar Terms 51
6.6 Monomials, Binomials, Trinomials, and Polynomials 52
6.7 Subscript and Prime Notations 52
6.8 Substitution of Numerical Values and Evolution 52
6.9 Algebraic Addition 53
6.10 Algebraic Subtraction 54
6.11 Addition of Polynomials 55
6.12 Subtraction of Polynomials 56
Summary 57
Chapter 7. Algebraic Multiplication of Monomials and Polynomials 59
7.1 Introduction 59
7.2 Multiplication of Signed Numbers 59
7.3 Multiplication of Signed Numbers with Exponents 61
7.4 Multiplication of Monomials Containing Exponents 62
7.5 Multiplication of Polynomials by Monomials 62
7.6 Multiplication of a Polynomial by Another Polynomial 63
Summary 65
Chapter 8. Division of Monomials and Polynomials 66
8.1 Introduction 66
8.2 Subtraction of Exponents 66
8.3 Division of Monomials 68
8.4 Division of a Polynomial by a Monomial 70
8.5 Division of a Polynomial by Another Polynomial 71
Summary 73
Chapter 9. Equations and Formulas 74
9.1 Introduction 74
9.2 Axioms for the Solution of Equations 74
9.3 Rules for the Solution of Equations 76
9.4 Mathematical Statements of Circuit Problems 78
Summary 80
Chapter 10. Factors of Algebraic Expressions 81
10.1 Introduction 81
10.2 Powers and Roots of Monomials 81
10.3 Monomial Factors of Polynomials 84
10.4 Calculation of the Square of a Binomial 85
10.5 The Product of Two Binomials 87
10.6 Extraction of the Square Root of a Trinomial 88
10.7 The Difference of Two Algebraic Numbers 88
10.8 Prime Factors of Polynomials 89
10.9 Factors of Trinomials 89
Summary 91
Chapter 11. Operations on Algebraic Fractions 92
11.1 Degrees of Monomials and Polynomials 92
11.2 Highest Common Factors of Monomials and Polynomials 92
11.3 Lowest Common Multiples of Monomials and Polynomials 94
11.4 Numerators and Denominators of Algebraic Fractions 95
11.5 Conversion of Mixed Expressions to Fractions and Vice-Versa 97
11.6 Lowest Common Denominator of Algebraic Fractions 98
11.7 Addition, Subtraction, Multiplication, and Division 100
11.8 Ratios and Quotients 103
11.9 Properties of Proportions 103
Summary 105
Chapter 12. Fractional Equations 106
12.1 Introduction 106
12.2 Series-Parallel Resistive Networks 110
Summary 114
Chapter 13. Network Theorems 115
13.1 Introduction 115
13.2 Thevenin's Theorem 115
13.3 Voltage-Divider Rule and Thevenin's Theorem 117
13.4 Norton's Theorem 118
Summary 120
Chapter 14. Simultaneous Equations and Graphical Solutions 121
14.1 Introduction 121
14.2 Rectangular or Cartesian Coordinates 122
14.3 Graphical Solutions of Equations 122
14.4 Algebraic Solution of Simultaneous Equations 124
14.5 Three Simultaneous Equations in Three Unknowns 128
14.6 Basic Determinants 128
Summary 131
Chapter 15. Complex Algebra 132
15.1 Introduction 132
15.2 Geometrical Representation of Imaginary Numbers 132
15.3 Pure Imaginary Numbers 133
15.4 Complex Numbers and Operations 134
Summary 137
Chapter 16. Logarithms 138
16.1 Introduction 138
16.2 Common Logarithms 138
16.3 Antilogarithms 139
16.4 Multiplication and Division by Logarithms 139
16.5 Evolution of Numbers by Logarithms 140
16.6 Applications of Common Logarithms 140
16.7 Decibel Reference Levels 141
16.8 Frequency Response and Decibel Gain 142
16.9 Filter Concepts and the Bode Plot 143
16.10 Band-Pass Filter Circuits 144
Summary 149
Chapter 17. Natural Logarithms and Exponential Functions 150
17.1 Introduction 150
17.2 Natural Logarithms 152
17.3 Inductance and Exponential Formulas 153
Summary 155
Chapter 18. Fundamentals of Trigonometry 156
18.1 Angular Notation 156
18.2 Trigonometric Functions 158
18.3 Trigonometric Functions of 30°, 45°, and 60° 159
18.4 General Angles 160
Summary 162
Chapter 19. Vector Fundamentals 163
19.1 Introduction 163
19.2 Periodic Functions 163
19.3 Vector Notations 165
19.4 Applications of Vectors 166
Summary 167
Chapter 20. Principles of Alternating Currents 168
20.1 Introduction 168
20.2 Voltage Relations in a Sine Wave 169
20.3 Capacitors in A-C Circuits 171
20.4 Power Relations in Capacitor Circuits 172
20.5 Capacitors Connected in Series 172
20.6 Resistance and Capacitance Connected in Series 173
20.7 Principles of Inductive Reactance 175
20.8 Resistance and Inductance Connected in Series 175
20.9 Admittance and Susceptance 176
20.10 Analysis of Parallel A-C Circuits 177
20.11 Resistance and Capacitance Connected in Parallel 178
20.12 Resistance and Inductance Connected in Parallel 180
20.13 The j Operator Notation 180
20.14 Analysis of Series-Parallel LCR Circuits 182
20.15 Analysis of Series-Parallel Circuits 184
20.16 Analysis of Series-Parallel LCR Circuits 186
Summary 189
Chapter 21. Boolean Algebra 190
21.1 Introduction 190
21.2 Boolean Addition and Multiplication 190
21.3 Logic Expressions and Symbology 191
21.4 Rules and Laws of Boolean Algebra 193
21.5 Theorems for Boolean Algebra 194
21.6 Demorgan's Theorems 196
21.7 KARNAUGH Maps 198
21.8 Entering Boolean Equations in a KARNAUGH Map 198
21.9 Simplification of Boolean Equations 199
Summary 202
Answers for Basic Electronics Math 204
Index 216