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chapter
8
BITS &
THE “WHY” OF BYTES
Digital Information 
digits are symbols
Digitizing Information: Symbols
Binary:0, 1
Decimal: 0, 1, 2, .. , 8, 9
Hexadecimal: 0, 1, .. , 9, A, B, C, D, E, F
Dice:
Coins:
Sidewalks:
Slide 8-2
The FUNDAMENTAL
Representation of Information
The Binary World (1and0)
joins the
Logical World (TandF)
&
Physical World (PandA)
Slide 8-3
The FUNDAMENTAL
Representation of Information
(p. 212)
By associating True with Presence &
False with Absence, we can use the
physical world to implement the
logical world.
Physical World (PandA):
solid/space; light/dark; on/off . . .
Slide 8-4
THE FUNDAMENTAL
REPRESENTATION OF INFORMATION
The PandA Representation
On_and_Off
 Binary: two states  two symbols
 Atom of Information: Irreducible
(eg) Bits in Optical Discs
—pits and lands
(eg) Bits in Magnetic Media
— North_and_South polarity
Slide 8-5
THE FUNDAMENTAL
REPRESENTATION OF INFORMATION
(eg) Bits in Old North Church
— One_and_Two
(eg) Bits in Computer Memory
 electronic
 transistors, integrated circuits
 device level
Slide 8-6
Digital Information: Dice Symbols
Base-6: Six “digits”, Six Symbols
{1, 2, .., 5, 6}
n dice => 6n different combinations
Slide 8-7
Figure 8.2. n = 2  62
patterns/combinations
Slide 8-8
Figure 8.3. Initial assignment of
letters to the dice-pair symbols.
Slide 8-9
Figure 8.4. Two complete dicepair representations. (Note: b
indicates a space.)
Slide 8-10
Extended Dice Code: Escape
Box Cars: Escape from
the Basic Repr.
Escape
A = 0
Slide 8-11
Extended Dice Code: Escape
Reserving one symbol as
an escape char
35 basic patterns
+ 35 two-symbol
patterns
esc sequences: 4 dice
Slide 8-12
Bit Sequences / Bit Patterns
> Table 8.2: the number of patterns given
the length of the sequence
> Generalizing:
base ^ pattern_length = number of patterns
 size of alphabet
Slide 8-13
HEX EXPLAINED
> The 16 Hex Digits: 0 .. 9, A .. F
> Hex explained: Table 8.3, p. 217
> Changing Hex Digits to Bits and Back Again
Slide 8-14
Figure 8.5. Magnetic media (hard
disk, tape, etc.)
pluses (red) indicate magnetism
of positive polarity, interpreted
as “present” and minuses (blue)
Slide 8-15
Figure 8.6. Sidewalk sections as
a bit pattern: 10100010
Slide 8-16
Slot Machine Symbols
Each roller has five symbols , hearts,
diamonds, spades, horseshoes, and three
liberty bells for jackpot.
3 rollers, 5 symbols
 ?number of patterns?
Slide 8-17
Binary Numerals: Ancient
Gottfried Leibniz (1703):
* Discovered calculus independently of
Newton, and his notation is the one in
general use since.
* Also discovered & organized the modern
binary number system
* first major European intellect to take a
close interest in Chinese civilization
Slide 8-18
Binary Numerals: Leibniz
64 hexagrams analogous to 6bit binary numerals,
comprise the ancient
Chinese classic text called
the I Ching
Leibniz noted with
fascination how the I Ching
hexagrams correspond to
the binary numbers from 0
to 111111
Slide 8-19
DIGITIZING TEXT
Extended ASCII: An 8-bit Code
 28 characters max
(eg) ASCII Encoding of Phone Numbers
x3487
Slide 8-20
Fig 8.7 ASCII, American Standard
Code for Information Interchange
Slide 8-21
THE OXFORD ENGLISH
DICTIONARY
Structure Tags == markup language
-- candidate for an XML application
(like XHTML)
 OEDML
Figure 8.8. The OED entry for the word
byte, together with the representation of
the entry in its digitized form with tags.
Slide 8-22
Slide 8-23