1. Chapter 3 Data Representation

2. Chapter 3 Data Representation
Chapter Outline
Data Representation and Processing
Automated Data Processing
Binary Data Representation
Goals of Computer Data Representation
CPU Data Types
Integer
Real number
Character
Boolean
Memory address
Technology Focus:
Intel Memory Address Format
Data Structures

3. Chapter Goals
Describe numbering systems and their use in data representation
Compare and contrast various data representation methods
Describe how nonnumeric data is represented
Describe common data structures and their uses

4. Data Representation and Processing
Capabilities required of any data/information processor–organic, mechanical, electrical, optical:
Recognizing external data and converting it to an appropriate internal format
Storing and retrieving data internally
Transporting data among internal storage and processing components
Manipulating data to produce desired results or decisions

5. Automated Data Processing
Data is converted from native format into a form suitable for the processing device
Computers represent data electrically and process it with electrical switches
Laws of electricity can be stated as mathematical equations
Electronic devices perform computational functions embedded in the equations

6. A + B = C
Example Circuit

7. Binary Data Representation
Binary number
Only one of two possible values (0 or 1) per digit
Reliably transported among computer system components
Can be processed by two–state electrical devices (relatively easy to design and fabricate)
Correspond directly with values in Boolean logic

11. Hexadecimal Notation
Uses 16 as its base or radix (hex = 6, and decimal = 10)
Compact; advantage over binary notation
Often used to designate memory addresses

12. Hexadecimal Notation

13. Octal Notation Uses base 8 numbering system
Has a range of digits from 0 to 7
Expresses large numeric values in:
One-third the length of corresponding binary notation
Double the length of corresponding hexadecimal notation

14. Goals of Computer Data Representation
Computer data formats are subject to trade-offs between several factors, including
Compactness
Accuracy
Range
Ease of manipulation
Standardization
Cost

15. Goals of Data Representation Compactness (Size)
Describes number of bits used to represent a numeric value
Trade-off: hardware cost vs. range of values
Fewer bits limits the range of values that can be represented
More bits requires increased cost in computer hardware to represent numbers
216 = ,53510
232 = ,294,967,29610
264 = 18,446,744,073,709,551,61610

16. Goals of Data Representation Accuracy (Precision)
Precision of representation increases with number of data bits used
Trade-off: hardware cost vs. precision
Fewer bits limits the precision of values that are represented
More bits requires increased cost in computer hardware to represent numbers precisely
Calculations can easily produce numbers too big or too small to represent precisely
So, they are represented as approximations that have a predictable error

17. Goals of Data Representation Ease of Manipulation
Machine efficiency increases when processing shorter and simpler numeric formats
Trade-off: processing time vs. precision
Processor efficiency depends on its complexity
Shorter and simpler formats require simpler circuitry
More precise formats require increased cost in computer hardware to process instructions

18. Goals of Data Representation Standardization
Standardized data formats increases speed and accuracy of data communications
Trade-off: processing time vs. networking
The most efficient circuitry may require non-standard data formats
To share information between a wide variety of devices, standardized data formats need to be used

19. CPU Data Types Primitive data types Integer Real number Character
Boolean
Memory address
Representation format for each type balances compactness, accuracy, ease of manipulation, and standardization

20. Memory Addresses
Identifying numbers of memory bytes in primary storage
Simple or complex numeric values depending on memory model used by CPU
Flat memory addresses
single integer
Segmented memory addresses
multiple integers
requires definition of specific coding format

21. Intel Memory Address Formats
8088
20-bit memory addresses
4-bit segment identifier
16-bit segment offset
80286
24-bit memory addresses
8-bit segment identifier
80386
32-bit memory addresses
16-bit segment identifier
80486
Pentium

22. Data Structures
Related groups of primitive data elements organized for a type of common processing
Defined and manipulated within software
Many use pointers to link primitive data components

23. Commonly Used Data Structures
arrays
linked lists
records
tables
files
indices
objects

24. One Address Finds Many Data Elements

25. Pointers and Addresses
Data element that contains the address of another data element
Address
Location of a data element within a storage device

26. Arrays and Lists List A set of related data values Array
An ordered list in which each element can be referenced by an index to its position

27. A simple array is used to store words

28. Linked Lists
Data structures that use pointers so list elements can be scattered among nonsequential storage locations
Singly linked lists
Doubly linked lists
Easier to expand or shrink than an array

29. A Singly Linked List

30. A Singly Linked List

31. Editing An Array

32. Editing A Singly Linked List

33. A Doubly Linked List

34. Records and Files Records
Data structures composed of other data structures or primitive data elements
Used as a unit of input and output to files
Files
Sequence of records on secondary storage

35. A Record Data Structure

36. Methods of Organizing Files
Sequential
Stores records in contiguous storage locations
Indexed
An array of pointers to records
Efficient record insertion, deletion, and retrieval

37. An Indexed File

38. Classes and Objects Classes
Data structures that contain traditional data elements and programs that manipulate that data
Combine related data items and extend the record to include methods that manipulate the data items
Objects
One instance, or variable, of the class

39. A Class of Objects

40. Summary How data is represented and stored within computer hardware
How simple data types are used as building blocks to create more complex data structures (e.g., arrays, records)
Understanding data representation is key to understanding hardware and software technology

41. Chapter Goals
Describe numbering systems and their use in data representation
Compare and contrast various data representation methods
Describe how nonnumeric data is represented
Describe common data structures and their uses