Number Systems and Programming

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Number Systems and Programming

• Data and Computers
• -all data used by computers is stored as bits
• -each bit is either a 0 or 1 Binary Code.
• -Computers operate in binary data is manipulated
  as collections of individual bits.
• -8 bits 1 byte
• -1 byte can represent numbers from 0 to 255.
• -Bytes can be combined to represent larger
  numbers.

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High-level languages

• When writing programs in high-level languages
  such as Turing, the base 10 number is used for
  convenience.
• Before the computer can use these numbers, they
  must be converted into binary form.

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Low-level languages

• Machine language and assembly Binary (base 2) or
  hexadecimal (Base 16)
• 4 binary digits 1 hexadecimal digit
• Hexadecimal Code
• 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
• Octal System (Base 8)
• 0,1,2,3,4,5,6,7

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Character Presentation System

• System required that can represent all letters,
  digits and special symbols.
• Presentation system must be agreed upon by all
  computers.

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ASCII baby!

• American Standard Code for Information
  Interchange
• 7 bits 128 symbols where
• A 65 100001
• A97

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ANSI

• American National Standards Institute
• 8 bits256 symbols
• First 128 are the same as ASCII
• Handles special characters in French and other
  European languages.

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EBCDIC

• Extended Binary Coded Decimal Interchange Code
• 8 bit system used on IBM mainframe computers
• Can only handle standard characters

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Unicode

• Universal Code
• 16 bit code
• Handles 65,536 symbols
• Handles all world languages

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Binary Mathbinary addition

• 0 0 0
• 0 1 1
• 1 0 1
• 1 1 10

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Binary Subtraction

• Direct method
• 0 0 0
• 1 0 1
• 1 1 1

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Binary subtraction

• 2s complement and Add 1
• 101 101
• -100 0111 100
• ------- -------
• 1001
• ------- -------

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Multiplying in Binary

• 0 0 0
• 0 1 0
• 1 0 0
• 1 1 1
• 10001 11110 111111110
• Try it

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Dividing in Binary

• 1/1 1
• 0/1 0
• 1/0 undefined
• 0/0 undefined

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Go to Assignment 6

• Please provide a problem definition, a flowchart
  and the code in Turing for the Number Converter
  program.
• May the programming force be with you.
• The end

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