Slide 8-2
Digitizing Information: Symbols
Binary:0, 1Decimal: 0, 1, 2, .. , 8, 9Hexadecimal: 0, 1, .. , 9, A, B, C, D, E, F
Dice:
Coins:
Sidewalks:
Slide 8-3
The FUNDAMENTAL Representation of Information
The Binary World (1and0)joins the
Logical World (TandF)&
Physical World (PandA)
Slide 8-4
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 8-5
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 8-6
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 8-7
Digital Information: Dice Symbols
Base-6: Six “digits”, Six Symbols{1, 2, .., 5, 6}
n dice => 6n different combinations
Slide 8-12
Extended Dice Code: Escape
Reserving one symbol as an escape char
35 basic patterns
+ 35 two-symbol patterns
esc sequences: 4 dice
Slide 8-13
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 8-14
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 8-15
Figure 8.5. Magnetic media (hard disk, tape, etc.)
pluses (red) indicate magnetism of positive polarity, interpreted as “present” and minuses (blue)
Slide 8-17
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 8-18
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 8-19
Binary Numerals: Leibniz
64 hexagrams analogous to 6-bit 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 8-20
DIGITIZING TEXT
Extended ASCII: An 8-bit Code 28 characters max
(eg) ASCII Encoding of Phone Numbersx3487
Slide 8-22
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.
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