Ch. 7 FIT5, CIS 110 13F

Chapter 7
Representing Information Digitally

Monday, October 28, 13

“Bits of Theory/Bytes of Practice”
-- A.K. Dewdney
Logic is the foundation of both reasoning
and computing.
By associating true with presence & false
with absence, we can use the physical
world [signals] to model the logical world
(symbols), and vice-versa.
This [is the Fundamental Principle of]
Information Technology.
-- p. 195, Ch. 8, FIT5
Copyright © 2013 Pearson Education, Inc. Publishing as Pearson Addison-Wesley


Fundament Principle of IT
Logic is the foundation of both reasoning
and computing.

Web Field Trip
Logic Gates: Logical AND
(http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/and.html)

=> Nine Rungs of the IT Inferno
(http://ix.cs.uoregon.edu/~michaelh/110/inferno.html)



Digitizing Information
• represent information with digits
• Digit: 0 .. 9 (Decimal Digit)
• Digitizing: use whole numbers as symbols
• BIT: 0 .. 1 (BInary digiT)
• Hex Digit: 0 .. 9, A .. F



Fundamental Information
Representation
• Computers: combine the physical (actual)
world with the logical (virtual) world
• Representation => from signal to symbol
• Physical world: the most fundamental form
of information is presence or absence
– P/A, On/Off, 1/0, T/F



Fundamental Information
Representation
• In the logical world, concepts of true (T)
and false (F) are important
• Logic: foundation of reasoning
• Logic: foundation of computing
• The physical world (machines) can
represent the logical world by associating
“true” with the Presence of a phenomenon
and “false” with its Absence


The PandA Representation
• PandA: the code used for two bits of
physical information:
– Presence
– Absence



The PandA Representation
• The presence or absence can be viewed
as “true” or “false”
• Such a formulation is said to be discrete
vs. continuous
• Signals are continuous
• Symbols are discrete



A Binary System
• The PandA encoding
has two bits: present &
absent
• Two bits make binary
• There is no law that
says on means
“present” or off
means “absent”
– convention
– interpretation


Bits Form Symbols
• The PandA unit is a bit
“binary digit”
• Bit sequences can be interpreted as
numbers or other information
• Groups of bits can represent symbols
– (eg) ASCII Character Code



Bits in Computer Memory
• Memory is arranged inside a computer in a
very long sequence of bits
• Memory locations are electronic (RAM)
• Bits are stored as Presence/Absence
• Symbolic representation: 1/0


Sidewalk Memory
• sidewalk: strip of concrete with lines across
it forming squares
• presence of a stone: 1
• absence of a stone: 0
=> sidewalk: a sequence of bits



Sidewalk Memory



Sidewalk Memory
0
1
0
1



0

0

1 0

Sidewalk Memory
• To write a 1: put a stone on a square
• To write a 0: sweep the sidewalk square
clean



Alternative PandA Encodings
• There is no limit to the ways to encode two
physical states
• “One if by land, Two if by sea.”
– Paul Revere Code
– Binary

• Git, Whoa!
– Conestoga Code
– Binary


Encoding Information w/ Bit
Patterns
• bit patterns of length 1:
=> encode 2 symbols
=> encode 4 symbols
=> encode 8 symbols
...
• bit patterns of length n:
=> 2n symbols
• adding 1 bit doubles number of
patterns


Bit Patterns of Length 4 = One Hex Digit



Hex Digits Explained
• hexadecimal digits are base-16 numbers
(24 = 16)
• using bit patterns is tedious & error prone
1111 1111 1001 1000 1110 0010 1010 1101
• one hex digit = 4 bits
=> shorthand representation
FF98E2AD


Hex to Bits and Back Again
• Easy to translate between hex and binary
– 0010 1011 1010 1101
2
B
A
D
–

F
A
B
4
1111 1010 1011 0100



Digitizing Numbers using Binary
• The two earliest uses of PandA were to:
– Encode numbers
– Encode keyboard characters

• Same principles apply to sound, images,
video, etc.



Decimal Numbers, Place Values
•
•
•
•

numbers use a place value representation
each “place” represents a power of 10
(binary numbers use powers of 2)
1,010 in decimal:



Binary Numbers, Place Values
• 10102
= (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1)
= 1010



Binary Numbers, Place Values
1,01010 = 0011 1111 00102



Digitizing Text
• The number of bits determines the number
of symbols that can be represented
– bit patterns of length n
=> 2n symbols

• The more symbols you want encoded, the
more bits you need



Digitizing Text (Characters)
• To represent 95 distinct symbols
• uppercase, lowercase, digits, punctuation,
etc.
• we need 7 bits
– 26 = 64 symbols
– 27 = 128 symbols

• plus additional characters
=> ASCII-8 Character Code
– 28 = 256 symbols


Extended ASCII: An 8-Bit Code
• Handling other languages is solved in two
ways:
– ASCII-8
– Unicode-16

• IBM named 8-bit sequence a byte
• ASCII-8: One Byte/One Character
• RAM: one memory location = 4 Bytes



Why “Byte”?
• IBM was building a supercomputer, called
Stretch
• They needed a word for a quantity of
memory between a bit and a word
• A word of computer memory is currently 32
bits



Why “Byte”?
• Then, why not bite?
• The ‘i’ to a ‘y’ was done so that someone
couldn’t accidentally change ‘byte’ to ‘bit’
by the dropping the ‘e’ ”
– bite
– byte

bit
byt

(the meaning changes)
(what’s a byt?)



Ch. 7 Assessment:
Learning Outcomes - Know the following



Ch. 7 FIT5, CIS 110 13F

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Ch. 7 FIT5, CIS 110 13F