Digital IT
Bits & Bytes
Digital Information 
digits are symbols
Computers =
automated symbol systems
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:
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The FUNDAMENTAL
Representation of Information
The Binary World (1and0)
joins the
Logical World (TandF)
&
Physical World (PandA)
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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 . . .
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Science historian & author George
Dyson:
The stored-program computer, as
conceived by Alan Turing and
delivered by John von Neumann,
broke the distinction between
numbers that mean things and
numbers that do things. Our universe
would never be the same.
Math: numbers mean things -> declarative
Computation: numbers do things ->
procedural epistemology
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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
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THE FUNDAMENTAL
REPRESENTATION OF INFORMATION
(eg) Bits in Old North Church
— One_and_Two
(eg) Bits in Computer Memory
è electronic
è transistors, integrated circuits
è device level
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Digital Information: Dice Symbols
Base-6: Six “digits”, Six Symbols
{1, 2, .., 5, 6}
n dice => 6n different combinations
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Figure 8.2. n = 2  62
patterns/combinations
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Figure 8.3. Initial assignment of
letters to the dice-pair symbols.
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Figure 8.4. Two complete dicepair representations. (Note: b
indicates a space.)
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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
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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
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Figure 8.5. Magnetic media
(hard disk, tape, etc.)
pluses (red) indicate magnetism
of positive polarity, interpreted
as “present” and minuses (blue)
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Figure 8.6. Sidewalk sections as
a bit pattern: 10100010
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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?
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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
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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
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DIGITIZING TEXT
Extended ASCII: An 8-bit Code
 28 characters max
(eg) ASCII Encoding of Phone Numbers
x3487
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Fig 8.7 ASCII, American Standard
Code for Information Interchange
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