D.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 D.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. D.8.

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

(This item is displayed on page 1240 in the print version)

Converting a binary number to decimal

Positional 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. D.9.

Figure D.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. D.10.

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

Converting a hexadecimal number to decimal

Positional 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


Introduction to Computers, the Internet and World Wide Web

Introduction to C++ Programming

Introduction to Classes and Objects

Control Statements: Part 1

Control Statements: Part 2

Functions and an Introduction to Recursion

Arrays and Vectors

Pointers and Pointer-Based Strings

Classes: A Deeper Look, Part 1

Classes: A Deeper Look, Part 2

Operator Overloading; String and Array Objects

Object-Oriented Programming: Inheritance

Object-Oriented Programming: Polymorphism

Templates

Stream Input/Output

Exception Handling

File Processing

Class string and String Stream Processing

Web Programming

Searching and Sorting

Data Structures

Bits, Characters, C-Strings and structs

Standard Template Library (STL)

Other Topics

Appendix A. Operator Precedence and Associativity Chart

Appendix B. ASCII Character Set

Appendix C. Fundamental Types

Appendix D. Number Systems

Appendix E. C Legacy Code Topics

Appendix F. Preprocessor

Appendix G. ATM Case Study Code

Appendix H. UML 2: Additional Diagram Types

Appendix I. C++ Internet and Web Resources

Appendix J. Introduction to XHTML

Appendix K. XHTML Special Characters

Appendix L. Using the Visual Studio .NET Debugger

Appendix M. Using the GNU C++ Debugger

Bibliography



C++ How to Program
C++ How to Program (5th Edition)
ISBN: 0131857576
EAN: 2147483647
Year: 2004
Pages: 627

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