ITE 272 Intro to ITE Part II

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ITE 272 - Intro to ITE Part II

• Chapter 3
• Data Representation

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Data Representation and Processing

• All processors must be able to
• Recognize external data / convert to internal
  format
• Store / retrieve internal data
• Transport data internally
• Manipulate internal data

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Binary Data Representation

• Stores data as
• True / false
• Yes / no
• On / off
• High / low

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Binary Data Representation

• Why do computers use binary?
• Can easily be represented as an electrical signal
• Can be reliably transported
• Among computer system components
• Processed by two-state electrical devices
• Easy to design
• Easy to build

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Binary Data Representation

• Why use?
• Corresponds directly to Boolean logic
• AND
• OR
• NOT
• XOR

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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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Numbering System Characteristics

• 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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Numbering System Characteristics
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Numbering System Characteristics
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Numbering System Characteristics
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Numbering System Characteristics

• 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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Numbering System Characteristics
Hexadecimal and decimal values
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Numbering System Characteristics

• 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)

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Goals of 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 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 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 (ex 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
Excess notation using four bits
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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

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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 Coding Methods

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

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CPU Data Types Coding Methods

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

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CPU Data Types Coding Methods

• 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 Coding Methods

• Unicode
• Multilingual character encoding standard
  encompassing all of the worlds written
  languages.
• Characters are coded using 16 bit strings.
• 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

• What is a data structure?
• Group of primitive data elements
• Defined / manipulated by software
• Hardware cannot directly manipulated
• Done in hardware via primitive data types
• Uses primitive data elements to create a new data
  type

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Data Structures
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Data Structures
Array Elements
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Data Structures
Character Array
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Data Structures
Linked List (Singly)
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Data Structures
Noncontiguous Character Array
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Data Structures
Linked List Insertion
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Data Structures
Insertion into Character Array
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Data Structures
Doubly Linked List
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Data Structures
Record (Data Structure)
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Data Structures
Indexing of Records
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The End