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Binary Notation. The world reduced to 0’s & 1’s. What are binary numbers?. Decimal system uses ten symbols to represent numeric information 0 1 2 3 4 5 6 7 8 9 Each position within a number represents 10 raised to a power

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binary notation

Binary Notation

The world reduced to 0’s & 1’s

what are binary numbers
What are binary numbers?
  • Decimal system uses ten symbols to represent numeric information
  • 0 1 2 3 4 5 6 7 8 9
  • Each position within a number represents 10 raised to a power
  • Binary system uses two symbols to represent numeric information
  • 0 1
  • Each position within a number represents 2 raised to a power
  • Binary numbers can be converted to decimal numbers and vice versa
using binary numbers
Using binary numbers
  • Binary numbers can be used for mathematical operations
    • 101 + 110 = 1011
  • Binary numbers can be used to represent characters
    • Morse Code -
    • S ... U ..- S ... A .- N -.
binary symbol representation
Binary symbol representation
  • Two numbers/symbols can be represented in many ways
    • 0 1
    • On Off
    • True False
    • Yes No
    • Open Closed
binary boolean logic
Gottfried Wilhelm Liebniz

(1646 - 1716)

Logic from verbal state to absolute mathematical condition

Influenced by ‘I Ching’

George Boole

(1815 - 1864)

Boolean Algebra

Two Object

On / Off, True / False

Three Operations

AND / OR / NOT

Binary & Boolean Logic
why do computers use binary
Why do computers use binary?
  • Must have a way to represent data and instructions
  • Minimum representation uses two symbols
  • Binary is the smallest numbering system with only two symbols, 0 & 1
  • Binary numbers combined with Boolean logic create circuits capable of mathematical and logic operations
not every computer used binary
Not every computer used binary

The Eniac, Electronic Numerical Integrator and Computer, used a decimal system

binary symbol representation9

Binary symbol representation

There are five different ways to represent binary symbols within a computer

Some volatile - some more permanent

integrated circuits
Integrated Circuits
  • Electrical representation
  • Multiple transistors on silicon chip
      • Open - electricity can flow - 1
      • Closed - no electrical flow - 0
  • Volatile
  • CPU
  • Ram
wire connections
Wire Connections
  • Electrical representation
      • 1.8 volts (or greater) - 1
      • 0 volts - 0
  • Volatile
  • System bus
magnetic
Magnetic
  • Magnetic properties of iron oxide particles covering a surface
      • Particles in one direction - 1
      • Particles in opposite direction - 0
  • Non-volatile
  • Hard disk
optical
Optical
  • Reflective surface with burned areas
      • Burned - Pit -1
      • Not burned - Land - 0
  • Non-volatile
  • CD
  • DVD
solid state
Solid State
  • Trapped electrons in a grid pattern with gates
      • Open - 1
      • Closed - 0
  • Non-volatile
  • Flash Drive
how binary notation represents data
How binary notation represents data
  • Bit - binary digit
    • on / off, 1 / 0, true / false, open / closed
  • Byte - eight bits
    • Smallest unit for storing data
how binary notation represents data16
How binary notation represents data
  • Numeric data
  • Numbers in binary
  • Instructions
  • Coded patterns of 0’s & 1’s
  • Characters
  • Encoding systems
who is behind encoding
Who is behind encoding
  • Standards Organizations
  • The Unicode Consortium
  • American National Standards Institute - ANSI
  • Institute of Electrical and Electronics Engineers - IEEE
  • International Organization for Standardization - ISO
using binary notation for other data
Using binary notation for other data
  • Analog signal
    • Continuous waves
  • Digital signal
    • Set of numbers
    • Can be used to describe a wave
    • Can also be used to recreate a wave
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