Digital Information

digits are symbols

chapter 8 BITS &

THE “WHY” OF BYTES

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 8-8

Figure 8.2. n = 2 62

patterns/combinations

Slide 8-9

Figure 8.3. Initial assignment of letters to the dice-pair symbols.

Slide 8-10

Figure 8.4. Two complete dice-pair representations. (Note: b indicates a space.)

Slide 8-11

Extended Dice Code: Escape

Box Cars: Escape from the Basic Repr.

Escape A = 0

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 8-16

Figure 8.6. Sidewalk sections as a bit pattern: 10100010

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 8-21

Fig 8.7 ASCII, American Standard Code for Information Interchange

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.

Slide 8-23