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Binary Notation
The world reduced to 0’s & 1’s
What are binary numbers?
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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
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Binary numbers can be used for
mathematical operations
 101
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+ 110 = 1011
Binary numbers can be used to
represent characters
 Morse
 S ... U
Code ..- S ... A .- N -.
Binary symbol representation
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Two numbers/symbols can be
represented in many ways
0
1
 On
Off
 True False
 Yes
No
 Open Closed
Binary & Boolean Logic
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Gottfried Wilhelm
Liebniz
(1646 - 1716)
Logic from verbal state
to absolute
mathematical condition
Influenced by ‘I Ching’
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George Boole
(1815 - 1864)
Boolean Algebra
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Two Object
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On / Off, True / False
Three Operations
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AND / OR / NOT
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
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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
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Electrical representation
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Multiple transistors on silicon chip
 Open
- electricity can flow - 1
 Closed
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Volatile
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CPU
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Ram
- no electrical flow - 0
Wire Connections
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Electrical representation
 1.8
0
volts (or greater) - 1
volts - 0
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Volatile
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System bus
Magnetic
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Magnetic properties of iron oxide
particles covering a surface
 Particles
in one direction - 1
 Particles
in opposite direction - 0
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Non-volatile
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Hard disk
Optical
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Reflective surface with burned areas
 Burned
 Not
- Pit -1
burned - Land - 0
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Non-volatile
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CD
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DVD
Solid State
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Trapped electrons in a grid pattern
with gates
 Open
-1
 Closed
-0
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Non-volatile
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Flash Drive
How binary notation represents data
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Bit - binary digit
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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
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Instructions
 Coded patterns of 0’s & 1’s
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Characters
 Encoding systems
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Encoding Systems
ASCII
Unicode
American Standard for
Information Interchange
EBCDIC
Extended Binary Coded
Decimal Interchange Code
One Byte
Two Bytes
One Byte
256 possible
characters
65,000+ possible
characters
256 possible
characters
A = 0100 0001
A = 0000 0000 0100 0001
A = 1100 0010
DOS and Windows to
Windows 98
Windows NT, Windows
2000, Windows XP
IBM Mainframe
Who is behind encoding
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Standards Organizations
The Unicode Consortium
 American National Standards Institute
- ANSI
 Institute of Electrical and Electronics
Engineers - IEEE
 International Organization for
Standardization - ISO
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Using binary notation for other data
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Analog signal
 Continuous
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waves
Digital signal
 Set
of numbers
 Can be used to describe a wave
 Can also be used to recreate a wave