Ch. 7 FIT5, CIS 110 13F

Chapter 7Representing Information Digitally

Monday, October 28, 13

Copyright © 2013 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

“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



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)


http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/and.html




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


Copyright © 2013 Pearson Education, Inc. Publishing as Pearson Addison-WesleyMonday, October 28, 13


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


http://www.ascii-code.com/



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



10

10

00 1 0

Sidewalk Memory



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

• bit patterns of length 2:=> encode 4 symbols

• bit patterns of length 3:=> 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

F F 9 8 E 2 A D



Hex to Bits and Back Again

• Easy to translate between hex and binary

– 0010 1011 1010 1101 2 B A D

– F A B 41111 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




Copyright © 2013 Pearson Education, Inc. Publishing as Pearson Addison-WesleyMonday, October 28, 13


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 bit (the meaning changes)– byte byt (what’s a byt?)



Ch. 7 Assessment:Learning Outcomes - Know the following
