Computer Mathematics for Programmers

1 Number Systems


1.0 Introduction


1.1 Base Ten, or the Decimal System


1.2 Base Two, or the Binary System


1.3 Base Eight, or the Octal System


1.4 Base Sixteen, or the Hexadecimal System


1.5 Converting Decimal Numbers into Binary Numbers


1.6 Converting Decimal Numbers into Octal Numbers


1.7 Converting Decimal Numbers into Hexadecimal Numbers


1.8 Converting Binary Numbers into Hexadecimal Numbers


1.9 Converting Hexadecimal Numbers into Binary Numbers


1.10 Summary

Problem Set A

Problem Set B

Practice Exam


2 Arithmetic Operations


2.0 Introduction


2.1 Addition Tables


2.2 Addition in the Binary System


2.3 Addition in the Octal System


2.4 Addition in the Hexadecimal System


2.5 Subtraction in the Binary System


2.6 Subtraction in the Octal System


2.7 Subtraction in the Hexadecimal System


2.8 Summary

Problem Set A

Problem Set B

Practice Exam


3 Computer Arithmetic


3.0 Introduction


3.1 Integer Storage


3.2 Integer Arithmetic


3.3 Exponential Notation


3.4 Floating Point Storage


3.5 Floating Point Arithmetic


3.6 Round-off Errors


3.7 Summary

Problem Set A

Problem Set B

Practice Exam


4 Algorithms and Flowcharts


4.0 Introduction


4.1 Algorithms


4.2 Flowcharts


4.3 Decisions


4.4 Summary

Problem Set A

Problem Set B

Practice Exam


5 Selected Topics in Algebra


5.0 Introduction


5.1 Order of Operations


5.2 Evaluating Algebraic Expressions


5.3 Addition and Subtraction of Like Terms


5.4 Removing Parentheses by Using the Distributive Law


5.5 Solving Equations in One Unknown


5.6 Equations in Two Unknowns


5.7 Simultaneous Equations (Substitution Method)


5.8 Simultaneous Equations (Elimination by Addition)


5.9 Summary

Problem Set A

Problem Set B

Practice Exam


6 Sets


6.0 Introduction


6.1 Set Descriptions


6.2 The Empty Set and the Universal Set


6.3 Operations with Sets


6.4 Subsets


6.5 Venn Diagrams


6.6 Summary

Problem Set A

Problem Set B

Practice Exam


7 Logic


7.0 Introduction


7.1 Statements


7.2 Truth Tables


7.3 Expansion of Truth Tables


7.4 Computer Applications


7.5 Summary

Problem Set A

Problem Set B

Practice Exam


8 Boolean Algebra


8.0 Introduction


8.1 The Basis of Boolean Algebra


8.2 Simplifying Boolean Expressions


8.3 Veitch Diagrams


8.4 A Security System


8.5 A Final Comment on Simplifying Boolean Expressions


8.6 Switching Circuits


8.7 Summary

Problem Set A

Problem Set B

Practice Exam


9 Matrices


9.0 Introduction


9.1 Addition and Subtraction of Matrices


9.2 Multiplication by a Constant


9.3 Multiplication of Matrices


9.4 Row Reduction


9.5 Equations with Three Unknowns


9.6 Summary

Problem Set A

Problem Set B

Practice Exam


10 Graphing and Linear Programming


10.0 Introduction


10.1 Graph Paper


10.2 Tables


10.3 Systems of Equations


10.4 Introduction to Linear Inequalities


10.5 Systems of Inequalities


10.6 An Introduction to Linear Programming


10.7 Summary

Problem Set A

Problem Set B

Practice Exam


11 Statistics


11.0 Introduction


11.1 Collection of Data


11.2 Grouped Data


11.3 Measures of the Center (Averages)


11.4 Measure of Variation (Standard Deviation)


11.5 Probability


11.6 The Normal Probability Curve


11.7 Applied Problems


11.8 Summary

Problem Set A

Problem Set B

Practice Exam

Appendices

A Basic Programs

A.0 Introduction

A.1 BASE/BAS

A.2 CONVERT/BAS

A.3 UNIVAC/BAS

A.4 IBM/BAS

A.5 COMM/BAS

A.6 CAR/BAS

A.7 EQS/BAS

A.8 GAUSE/BAS

A.9 STAT/BAS

A.10 STATBAR/BAS

A.11 RNDNOR/BAS

A.12 SNT/BAS

B Tables

B.1 Addition

B.2 Powers of Two

B.3 Truth Tables

B.4 Normal Probability Table

C Glossary

D Answers to Problem Sets A and Practice Exams

Index