Data Representation

1
Data Representation

• Chapter 3

2
Objectives

• 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

3
Data Representation and Processing

• Data and information processors must be able to
• Recognize external data and convert it to an
  appropriate internal format
• Store and retrieve data internally
• Transport data among internal storage and
  processing components
• Manipulating data to produce results or decisions

4
Automated Data Processing

• Processing is implemented with electrical
  switches which are combined to form processing
  circuits.
• For Example A B C

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Automated Data Processing
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Binary Data Representation

• Computers use binary numbers
• Binary numbers correspond directly with values in
  boolean logic.
• Computers combine multiple digits to form a
  single data value to represent large numbers.

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Binary Data Representation

• Numbering System Characteristics
• The number of characters in the number system is
  equal to the base of the number system.
• There are 10 characters in the decimal number
  system. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
• There are 2 characters in the binary number
  system. (0, 1)

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Binary Data Representation
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Binary Data Representation

• The fractional part of a numeric value is
  separated from the whole number by a period
  (radix point)
• For Example 5,689.368
• (3 x .1) (6 x .01) (8 x .001)
• 0.3 0.06 0.008 0.368

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Binary Data Representation
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Binary Data Representation
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Binary Data Representation

• Hexadecimal Notation
• The base (radix) of a hexadecimal number system
  is 16.
• There are 16 characters in the hexadecimal number
  system.
• There are only 10 characters in the Arabic number
  system that can be used to represent some of the
  16 characters in the hexadecimal number system.
• The letters A, B, C, D, E, F are used to
  represent the last 6 characters in the
  hexadecimal number system.

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Binary Data Representation
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Binary Data Representation

• Octal Notation
• Some operating systems and machine language
  programs use octal notation.
• The base (radix) of an Octal number system is 8.
• There are 8 characters in the octal number
  system. (0, 1, 2, 3, 4, 5, 6, 7)

15
Goals of Computer Data Representation

• Compactness - compact data representation
  requires less storage space and less expensive
  processing and storage devices.
• Accuracy - the accuracy of representation
  increases with the number of data bits used.

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Goals of Computer Data Representation

• Range routine calculations can generate
  quantities that are either too large or too small
  to be stored within finite circuitry.
• Ease of manipulation - the efficiency of a
  processor depends on its complexity.

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Goals of Computer Data Representation

• Standardization - various organizations have
  created standard data encoding methods for
  communication among computer systems and their
  components.

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CPU Data Types

• Five Primitive Data Types
• Integer
• Excess Notation
• Twos Complement Notation
• Real number
• Floating Point Notation
• Character
• Boolean
• Memory address

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CPU Data Types

• Integer
• An integer is a whole number (For example 3, 5,
  6)
• Integers can be signed or unsigned
• A signed integer uses one bit to represent the
  sign
• The sign bit is the high order bit
• Excess notation is used to represent signed
  integers

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CPU Data Types
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CPU Data Types

• Twos Complement Notation
• Nonnegative integer values are represented as
  ordinary binary numbers
• Negative integer values are represented using
  (Complement of positive value 1)
• The complement of a number is formed by changing
  all 1 bits to 0 and all 0 bits to 1

22
CPU Data Types

• Real Numbers
• A real number can contain both whole and
  fractional components
• The whole portion appears to the left of the
  radix point
• The fractional portion appears to the right of
  the radix point

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CPU Data Types
Real Number
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CPU Data Types
Scientific Notation
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CPU Data Types

• Floating Point Notation
• Floating point notation is used to represent very
  small numbers and very large numbers
• Values can either be very large or very small,
  but not both at the same time

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CPU Data Types
Floating Point Notation
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CPU Data Types

• Character Data
• An individual symbol is a character.
• Characters grouped together form a string.
• Character data can only be represented in the
  computer system using a coding scheme.

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CPU Data Types

• Binary Coded Decimal (BCD)
• Character coding method used by early IBM
  mainframe computers.
• Characters are encoded as strings of six bits.
• 64 - (26) symbols are represented.

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CPU Data Types

• Extended Binary Coded Decimal Interchange Code
• 8 bit coding method used by IBM mainframe
  computers.
• Characters are encoded as strings of eight bits.
• 256 - (28) symbols are represented.

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CPU Data Types

• American Standard Code of Information
  Interchange
• Coding method used in data communication that has
  been adopted by the United States.
• 7-bit and 8-bit formats
• Includes device control codes

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CPU Data Types
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CPU Data Types

• Unicode
• Multilingual character encoding standard
  encompassing all of the worlds written
  languages.
• Characters are coded using 16 bit strings.
• 65,535 (216) characters are represented.

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CPU Data Types

• Boolean Data
• Two data values true and false.
• Data is represented using a single bit.
• Binary 1 can represent true and binary 0 can
  represent false.

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CPU Data Types

• Memory Addresses
• Flat memory model Memory addresses can be
  represented using a single integer.
• Segmented memory model
• Memory addresses require multiple integers.

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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Data Structures
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Summary

• To be processed by any device, data must be
  converted from its native format into a form
  suitable for the processing device.
• All data, including nonnumeric data, are
  represented within a modern computer system as
  strings of binary digits, or bits.
• Each bit string has a specific data format and
  coding method.

47
Summary

• Numeric data is stored using integer, real
  number, and floating point formats.
• Characters are converted to numbers by means of a
  coding table.
• Boolean values can have only two values, true and
  false.
• Data structures are used by programs to define
  and manipulate data in larger and more complex
  units than primitive CPU data types.