digression: binary addition representing characterssud/comp4/lectures/lecture07/lec07.pdf · 010 =...

Summer II 2005, Lec-07

COMP 4—Power Tools for the Mind 1What’s in the box?

Representing Concepts Part 2--What we’ll cover for Part 2 :

• Representing concepts in a computer– 1st type: Numeric values --brief review– Today: How are some of the other

concepts represented in the box?

1234


Information theory: Study of the most efficient way to encode concepts: information that interests us.– All information must be captured & stored, processed, and

transmitted.– Using numbers to represent information allows us to use a

discrete symbol system: distinct, unambiguous, precise.– Discrete numbers are much easier to engineer than

continuous numbers.

Quick review of Part 1:• How do we represent numeric values such as

1378 or 17.2351 in a computer?– Logical structure? Physical structure?– Mathematical operations (add, subtract, multiply,

divide) operate on numeric information.


Digression: Binary Addition

Sum:

1 0 1 1base 2

1 1 1 1base 2

0

1Carry:

1

1

0

1

11

Rules• 0 + 0 = 0• 1 + 0 = 0 + 1 = 1• 1 + 1 = 1 0


Representing characterscharacters

• With unique bit patterns, we can represent any character (including foreign characters), just the way we already used unique bit patterns to represent decimal values……

–Digression: the program determines if a stored bit pattern represents a numeric value, or an alphanumerictext, or part of a sound, or part of a picture, or part of an instruction.....

• A - Z a - z 0 - 9 ! @ # $ % ^ & * ( ) + =• Must work with binary coding schemes (why?)


• However: Bit patterns that represent characters(alphanumeric) are typically not used used for mathematical computations like add or subtract.

• Instead: alphanumeric characters are mostly used to store textual content, which may be sorted or concatenated.

• So: although both numeric values (used for counting & math) and alphanumeric characters(used for text) are both represented using a bit pattern, they are treated differently.

Another digression:


– Number characters (alphanumeric) are treated by the computer as text characters:• 9 not= “9”

• 9 + 9 = 18 while “9” + “9” = “99”

The Binary pattern that represents 9 is different from the binary pattern that represents “9”.

– yet sorting is possible because text characters also have a binary (numeric) value:

The numeric value of the binary representation of A is smaller than B and also B is smaller than C and so on …

Consider:



Letter BBin binary code

Letter BB“in the box”

128 64 32 16 8 4 2 1 “Place”“0” 0 1 0 1 0 0 0 0“1” 0 1 0 1 0 0 0 1“2” 0 1 0 1 0 0 1 0

“A” 0 1 0 0 0 0 0 1“B” 0 1 0 0 0 0 1 0

How to represent C C ??? NOTICE how A < B < C ……

“C” 0 1 0 0 0 0 1 1


Number of symbols possibleRemember?x bits could represent 2x numbers2 bits ⇒ 22 = 4 different bit patterns

4 bits? ⇒ 16 different

[24 = 16]

Bit pattern0000000100100011010001010110011110001001101010111100110111101111

Decimal value0123456789

101112131415

SAME THING when representingalphanumeric characters:A two-bit code (two bulbs) can represent(e.g. encode) four unique characters.


0 0= A

B0 1

=

C1 0

=

D1 1

=

22 = 4Base # bits = number

of unique combinations

(that represent values)


Base# of bits used = number of unique symbols thecoding scheme can represent

Bit pattern length

LOGICAL Representation (bit coding scheme):

#-of-States # of bulbs = number of unique symbols the bulbs can represent

How many bulbs (switches, transistors, vacuum tubes, magnetized locations on disk, ...)

PHYSICAL Representation (hardware “bits”):

CORRESPONDS DIRECTLY to the


What if we use more expensive light bulbs? OFF LOW HIGH

#-of-States # of bulbs = number of unique combinations; which indicates number of unique values the bulbs can represent

QUICK! Would that allow us to represent/encode MORE or LESS unique things? WHY? (assume will use only 2 bulbs)

0 0= A

B

C

D

0 1

0 2

1 0=

=

=

1 1= E

F

G

H

1 2

2 0

2 1

=

=

=

2 2= I

Then what has changed? Not how many bulbs, but what?

32 = 9 combinations COMP 4—Power Tools for the Mind 12What’s in the box?

What if we don’t want to use complicated bulbs---how else can we INCREASE how many things can be represented??So, base (# of states) is two: (0 , 1) (off , on) NOW what MUST change?

= H?1 1 1

1 1 00 0= A

0

0 0= B

1

0 1 0= C

0 1= D

1

1 0= E

0

1 0 1= F

= G

23 = 8 combinations

Base# of bits used = number of unique things thecoding scheme can represent

#-of-States # of bulbs = number of unique combinations; which indicates number of unique things the bulbs can represent



So, to get morethings

represented, we just keep adding bits

(or light bulbs)

22 = 4 combinations23 = 8 “24 = 16 “25 = 32 “26 = 64 “27 = 128 “28 = 256 “

216= 65536 “

.... ....


For alphanumeric character values:

Bit pattern0101 0000 0101 00010101 00100101 0011(etc)

0100 00010100 00100100 00110100 01000100 0101(etc)

Character (text) value0 123

(etc)

ABCDE

(etc)

7, 8, 16, 32, and 64-bit patterns are used for alphanumeric character values:

27= 128 character values

28= 256 character values

216= 65,536 character values

232= > 4 billion char values

264= 18,446,744,073,709,551,616 character values

14


Challenge 1: 26 upper-case characters in our alphabet. Want our electronic word processor to manipulate all 26.

2

What two parts of the equation do we already know?Base# bits used = no. of unique things coding scheme can represent

States# bulbs used = no. of unique things coding scheme “ “

– Must create binary coding scheme that will allow us enough unique patterns to encode all 26.

• What is the minimum bit pattern length that is required for our coding scheme? (minimum number of bulbs)

x=5 (25=32)>= 26 x


Challenge 2: there are X number of characters in Zuni alphabet. Want our word processor to manipulate all of them.

• A binary coding scheme, which is six bits long, would allow enough unique patterns to be able to manipulate all the characters of the Zuni alphabet.

• Maximum number of characters in the Zuni alphabet?

Base# of bits used = no. of unique things coding scheme can represent

What parts do we already know?

26 >= X X=64


• ASCII and Extended ASCII (ANSI):– Standard ASCII: Basic set for character data:

7-bit code• can represent how many characters?

– ANSI: Extended ASCII to 8-bits. (Windows apps use 8 bits)

• can represent how many characters?• 8 bits: each pattern also fits nicely into 1 memory cell.

128

256

Character formats


8-bit ASCII0 0101 00001 0101 00012 0101 0010A 0100 0001B 0100 0010C 0100 0011

Hello01001000 01100101 01101100 01101100 01101111In 8-bit ASCII code:

8 bits: one byte (one character): logical8 bulbs: stores one byte: physical

In the box (memory or storage):

17



• Other codes– Unicode: 16-bit code (65,536 bit patterns)– Internat’l Standards Org: 32-bit code (>4 billion

bit patterns)

Quotable...

Representing other information types… pictures, sounds


Important digression:– Data can travel and be stored in the form of a signal.

• Signal: anything that changes with time or space.

– Different types of signals: • Analog: continuous values (measurable)

– Most of what we see/hear is in ANALOG form: sound, light, water, electricity, temperature, wind: can be plotted as a continuous, undulating line or wave.

0 time

• Digital: discrete values (countable, like numbers)

0 time


Converting analog info to digital form:• Most natural forms of information (pictures,

sounds) are in analog form--continuous values– E.g.: Sound: how loud? How high? (pitch)– E.g.: Color: GRAY . But how GRAY is it?

• No precise way in analog world to determine this perfectly and the same each time. G G G G

• Computers: designed to store and process (and transmit) discrete, on/off signals.

• So with digital computers, we’ll have to change analog signals with infinite precision into digital signals with finiteprecision.

• That process is called “digitizing” (or “sampling”).


Advantages of digital (over analog)• Digital signals offer the following, and more…

– Known Precision – Ordinality (built-in order of numbers)

• Shades from darkest to lightest are expressed as numbers,from smallest to largest.

• Example: Eight shades to work with, from black to white:

0 1 2 3 4 5 6 7000 001 010 011 100 101 110 111

– Absolute perfect replication• Analog: Copy of a copy of a copy…..last as good as original?

– Content analysis much easier– Compression techniques work well (later!!)


Images; graphicsComputer images: formed by collections of

dots; each dot is a picture element: pixel. How image is represented & stored inside

the computer (logical structure) can be radically different.

1. Bitmapped: Also called Raster2. Object-oriented: Also called Vector– Each has its own advantages, disadvantages, and

particular uses.

Representing visual infovisual info • Bitmap graphics

Phys’l:Log’l: 000 001 010 011 100 101 110 111

0 1 2 3 4 5 6 7 Dec’lBinary

– Image is represented by bits.– Each bit pattern defines one pixel.– Good illustration: SCANNER

• Regular photograph. What kind of information is it?

• What kind of information can be stored and manipulated inside a digital computer?

• Essentially, then, what does your SCANNER have to do?

• In laymen’s terms, how?

23



– Stored representation of such a picture: “bitmap” or “pixmap”

• Stored bits are like a map of image being represented.

Physical representation of bits are actually stored in memory.

Bitmap

B&W Image

• Program? Knows nothing about shapes of objects; only which pixels are what color value (more shortly…)

24 COMP 4—Power Tools for the Mind 26What’s in the box?

– Monochrome (Black&White). • If a single pixel can

be either black orwhite, then how manybits are needed torepresent one pixel?

Why?

0 1

25

– Grayscale• What if we want to represent more? Say, shades of gray.

What has to happen to the bits stored in memory in order to represent more different values (shades) on the screen?

Intuitively: LESS or MORE bits/pixel than with B&W?• ILLUSTRATION: If a single pixel can be any one of

eight shades, what minimum # of stored bits is needed to represent that one pixel? (Length of coding scheme?)

000 001 010 011 100 101 110 111

OK, what about binary bits? Are two bits enough?2? = 8 unique “shades” (or values of gray)

00 01 10 11 ? ?0 1 2 3 4 5 6 7

262? = 256 unique “shades” (or values of gray) COMP 4—Power Tools for the Mind 28What’s in the box?

Editing bitmaps


Base# of bits used = number of unique concepts/valuesthe coding scheme can represent

Bit pattern lengthREMEMBER BACK?Number of shades possible

Base# of bits used = number of unique shades/colorsthe coding scheme can represent

Bit pattern length

NOTICE a PATTERN HERE ? 28 COMP 4—Power Tools for the Mind 30What’s in the box?

– Color Primary colors for computer graphics:RGB

– Digression: Why RGB?

For more information:Primary colors http://www.beer.org/~tpark/color.html

How colors work:http://www.rgbworld.com/color.html

The additive reproduction process mixes various amounts of R, G and B light to produce other colors.

Representing color

29



“True” color uses a 24 bit code to represent each color value: (photographic quality)

–8 bits for red (28 = 256 shades of red)–8 bits for green (28 = 256 shades of green)–8 bits for blue (28 = 256 shades of blue)

Combine various shades to make various color combinations (provides lots of bit patterns).

• SO: If one pixel is represented by a 24-bit code, how many different COLOR VALUES can a single pixel display?

224 = ? ~16.7 million unique color values.

8 bits 8 bits 8 bits

30 COMP 4—Power Tools for the Mind 32What’s in the box?

LOOKING IN THE BOX: 24 bits stored for EACH PIXEL!

000000000000000000000000 = BLACK

Again, imagine an advancing odometer that would show allof the color valuesbetween black and white …!

= All OFF

111111111111111111111111 = WHITE= All ON

000000000000000000000001000000000000000000000010000000000000000000000011000000000000000000000100000000000000000000000101000000000000000000000110000000000000000000000111000000000000000000001000

AND LOTS MORE!


– File format : How information is encoded & stored

– Different software apps understand different graphics file formats (encoding systems).

– TIFF, GIF, JPEG, BMP,... – Some better for certain purposes... Beyond the scope of COMP 4.

– When saving an image file one can usually choose a file format from a selection.

– PowerPoint, for example, recognizes a number of graphics file formats, but not all.

– However, utilities (filters) can interpret and convert one file format to another. Software often comes w/filters (or can download from software vendor’s Web site).

File formats for bitmap graphics


–Advantages, disadvantages, applications:

Original bitmapped

graphic

Same image scaled up

–Photo realism.–Software: Photo editing, and Paint.

–Can work at pixel level. –HUGE files without compression!

–Storage and download time!–Images do not scale up well:

–Image resolution is important


Vector graphics– Uses instructions to draw lines, fill shapes (rather

than tracking and storing bits for each pixel)…. In English: “Draw a circle at the point that is 100 pixels to the

right and 140 pixels down from the top-left corner of the screen with the radius of 25 pixels.”

– Software: Drawing. • Shapes are known to the program. Does not work at pixel

level, but rather at object-level.

– Scalable, no jaggies.– Files relatively small– Layering: “2 ½ dimensions”– Seeing more vector graphics for the Web: .sfv, .cmg


another important means of conveying information.– Produced by vibration; transmitted over a medium.

• Sound travels in analog wave patterns.• Wave characteristics: amplitude (loudness) and

frequency (pitch) can be measured & sampled over time, and stored as a sequence of binary numbers.

• Called? “Digitizing” or “sampling”– Much like scanning an analog photograph spatially

creates a digital bitmap.

• The higher the sampling rate, the better the quality of the digital signal!

Representing soundsound



• Captured in analog form by an analog microphone• Converted to digital form by an ADC (audio to digital converter)• Stored as file on a digital storage device (CD or hard drive). Then, for playback to human ears:• Converted to analog form by a DAC (digital to analog converter)• Played back by analog speakers.

Samples

0 time

dB

Samplingrate

Analog to digital audio

Analog sounds can be:


These days, we can get – Digital capture and player devices for both audio and

video.• Digital cameras• Digital camcorders• Digital microphones

– So, for that data, the computer does not need ADC or DAC converters:

captured and played all in the same digital mode.

• MP3 files: file format that squeezes digital sound into small files through sophisticated compression adapted to the human ear (more later). Fast to download; less to store.


SUMMARY!– We can use bit patterns of zeroes and ones to

represent:• Numeric values• Alphanumeric text• Pictures (bitmaps)• Soundsand• Instructions

– Vector graphics; MIDI (music); General programming (coming)

RECAP: SOFTWARE determines if a stored bit patternrepresents a numeric value, or alphanumeric text, or part of a sound, or part of a picture, or part of an instruction..... all bits look the same to the CPU!

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