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Binary Notation PowerPoint PPT Presentation


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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

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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

  • 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

  • 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

  • Two numbers/symbols can be represented in many ways

    • 0 1

    • On Off

    • True False

    • Yes No

    • Open Closed


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


How does Boolean Logic work?


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

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


Binary symbol representation

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

Some volatile - some more permanent


Integrated Circuits

  • Electrical representation

  • Multiple transistors on silicon chip

    • Open - electricity can flow - 1

    • Closed - no electrical flow - 0

  • Volatile

  • CPU

  • Ram


  • Wire Connections

    • Electrical representation

      • 1.8 volts (or greater) - 1

      • 0 volts - 0

  • Volatile

  • System bus


  • 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

    • Reflective surface with burned areas

      • Burned - Pit -1

      • Not burned - Land - 0

  • Non-volatile

  • CD

  • DVD


  • Solid State

    • Trapped electrons in a grid pattern with gates

      • Open - 1

      • Closed - 0

  • Non-volatile

  • Flash Drive


  • 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 data

    • Numeric data

    • Numbers in binary

    • Instructions

    • Coded patterns of 0’s & 1’s

    • Characters

    • Encoding systems


    Encoding Systems


    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

    • 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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