Introduction to Microcomputers

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Introduction to Microcomputers

• Computer numbering Systems

Prepared by Hani Al-Mohair
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Introduction to Binary Numbers

• How Computers Store Numbers
• Computer systems are constructed of digital
  electronics. That means that their electronic
  circuits can exist in only one of two states on
  or off. Most computer electronics use voltage
  levels to indicate their present state. For
  example, a transistor with five volts would be
  considered "on", while a transistor with no
  voltage would be considered "off." Not all
  computer hardware uses voltage, however.
  CD-ROM's, for example, use microscopic dark spots
  on the surface of the disk to indicate "off,"
  while the ordinary shiny surface is considered
  "on." Hard disks use magnetism, while computer
  memory uses electric charges stored in tiny
  capacitors to indicate "on" or "off."

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Cont.

• These patterns of "on" and "off" stored inside
  the computer are used to encode numbers using the
  binary number system. The binary number system is
  a method of storing ordinary numbers such as 42
  or 365 as patterns of 1's and 0's. Because of
  their digital nature, a computer's electronics
  can easily manipulate numbers stored in binary by
  treating 1 as "on" and 0 as "off." Computers have
  circuits that can add, subtract, multiply,
  divide, and do many other things to numbers
  stored in binary.

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Converting from Decimal to Binary

• Computer numbering Systems
• Decimal
• Binary
• Octal
• Hexadecimal.

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Binary Truth Table
De 8 4 2 1
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1

• 0 Off
• 1 On

Convert from decimal to binary (30) ? (56)
? (267) ?
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From Binary to Decimal

• Fill the blanks
• Computers use binary numbers and human use
  decimal numbers.

Convert from Binary to decimal (0111)2
? (0001)2? (1001)2? (1100)2? (1110)2?
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From Binary to Hexadecimal

• A 10 16 1C
• B 11 17 1D
• C 12 18 1E
• D 13 19 1F
• E 14 1A 20
• F 15 1B