B.4. Converting from Binary, Octal or Hexadecimal to Decimal

We are accustomed to working in decimal, and therefore it is often convenient to convert a binary, octal, or hexadecimal number to decimal to get a sense of what the number is "really" worth. Our diagrams in Section B.1 express the positional values in decimal. To convert a number to decimal from another base, multiply the decimal equivalent of each digit by its positional value and sum these products. For example, the binary number 110101 is converted to decimal 53, as shown in Fig. B.8.

Figure B.8. Converting a binary number to decimal.

Converting a binary number to decimal

Postional values:

32

16

8

4

2

1

Symbol values:

1

1

0

1

0

1

Products:

1*32=32

1*16=16

0*8=0

1*4=4

0*2=0

1*1=1

Sum:

= 32 + 16 + 0 + 4 + 0s + 1 = 53

To convert octal 7614 to decimal 3980, we use the same technique, this time using appropriate octal positional values, as shown in Fig. B.9.

Figure B.9. Converting an octal number to decimal.

Converting an octal number to decimal

Positional values:

512

64

8

1

Symbol values:

7

6

1

4

Products

7*512=3584

6*64=384

1*8=8

4*1=4

Sum:

= 3584 + 384 + 8 + 4 = 3980

To convert hexadecimal AD3B to decimal 44347, we use the same technique, this time using appropriate hexadecimal positional values, as shown in Fig. B.10.

Figure B.10. Converting a hexadecimal number to decimal.

Converting a hexadecimal number to decimal

Postional values:

4096

256

16

1

Symbol values:

A

D

3

B

Products

A*4096=40960

D*256=3328

3*16=48

B*1=11

Sum:

= 40960 + 3328 + 48 + 11 = 44347


Preface

Index

    Introduction to Computers, the Internet and Visual C#

    Introduction to the Visual C# 2005 Express Edition IDE

    Introduction to C# Applications

    Introduction to Classes and Objects

    Control Statements: Part 1

    Control Statements: Part 2

    Methods: A Deeper Look

    Arrays

    Classes and Objects: A Deeper Look

    Object-Oriented Programming: Inheritance

    Polymorphism, Interfaces & Operator Overloading

    Exception Handling

    Graphical User Interface Concepts: Part 1

    Graphical User Interface Concepts: Part 2

    Multithreading

    Strings, Characters and Regular Expressions

    Graphics and Multimedia

    Files and Streams

    Extensible Markup Language (XML)

    Database, SQL and ADO.NET

    ASP.NET 2.0, Web Forms and Web Controls

    Web Services

    Networking: Streams-Based Sockets and Datagrams

    Searching and Sorting

    Data Structures

    Generics

    Collections

    Appendix A. Operator Precedence Chart

    Appendix B. Number Systems

    Appendix C. Using the Visual Studio 2005 Debugger

    Appendix D. ASCII Character Set

    Appendix E. Unicode®

    Appendix F. Introduction to XHTML: Part 1

    Appendix G. Introduction to XHTML: Part 2

    Appendix H. HTML/XHTML Special Characters

    Appendix I. HTML/XHTML Colors

    Appendix J. ATM Case Study Code

    Appendix K. UML 2: Additional Diagram Types

    Appendix L. Simple Types

    Index



    Visual C# How to Program
    Visual C# 2005 How to Program (2nd Edition)
    ISBN: 0131525239
    EAN: 2147483647
    Year: 2004
    Pages: 600

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