CSCE101

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CSCE101 4.1, 4.2 and Number Systems

• October 5 10, 2006

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Study Tree
Part II
Binary Numbering System And Computing (4.2)
Computer as a State Machine (4.1)
Number System Conversions
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4.1 Microchips, Miniaturization Mobility

• Transistor key component in all modern
  electronics
• Vacuum tubes to discrete transistors to
  integrated circuitry
• Transistors
• Modulate electric current
• Act as switches
• Integrated circuit chip, contains other
  circuitry to control current

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4.1 Microchips cont.

• Microchip or chip contain millions of circuits
  (interconnections of electronic components)
• Circuitry is solid-state
• Circuitry is embedded on silicon
• Silicon is a semi-conductor
• Photolithography etches the circuit design onto a
  wafer in layers
• Wafer is cut into chips
• Chips are mounted in a protective frame

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4.1 Microchips cont.

• Different kind of chips RAM, ROM, CPU
• Circuitry is designed differently for various
  chips
• All are sets of transistors (switches) in on/off
  state at any given instant (panels of blinking
  lights, anemones)
• Computer is a state machine runs through a
  series of states to produce result.

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System to represent the state machine

• On-off, x-y, 1-0
• Number systems
• Decimal
• Base 20
• Octal
• Hexadecimal (Web pages, URLs)
• Binary

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In the machine

• Using binary to represent all of the following
• Data and Information (Numbers and Letters)
• Instructions
• Arithmetic operations
• Logical operations
• Error-checking (Parity Checking)
• Bit, byte, kilobyte, megabyte, gigabyte,
  terabyte, petabyte

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Representations

• Data and Information
• Numbers
• EBCDIC
• ASCII
• UNICODE

Binary Dec Hex Glyph
0100 0000 64 40 _at_
0100 0001 65 41 A
0100 0010 66 42 B
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Representations

• Data and Information
• Numbers
• EBCDIC
• ASCII
• UNICODE
• Instructions
• Each processor has its own representation of
  instructions (its own machine language)
• For example adding the registers 1 and 2 and
  placing the result in register 6 is encoded
• op rs rt rd shamt funct
• 000000 00001 00010 00110 00000 100000 binary
• 0 1 2 6 0 32
  decimal

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Conversions

• Binary to Decimal
• Binary to Hexadecimal
• Hexadecimal to Decimal
• Hexadecimal to Binary
• Decimal to Binary
• Decimal to Hexadecimal

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Representations (continued)

• Binary arithmetic
• Addition
• Subtraction
• Binary (Boolean) Logic
• George Boole
• Claude Shannon
• Propositional Logic
• if(B16gt600, Car payment can be made, Car
  payment cannot be made)

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System Unit

• Display
• Motherboard
• CPU (Microprocessor)
• Primary storage (RAM)
• Expansion cards
• Power supply
• Optical disk drive
• Secondary storage (HD)
• Keyboard
• Mouse