data representation robin burke it 130. outline data representation binary numbers image types

Data Representation

Robin Burke

IT 130

Outline

Data Representation Binary Numbers Image types

Apology

Errors The math in this chapter is full of errors

Number Systems A number system for n

Digits from 0 to n-1 kth position = factor of nk

Decimal (n=10) digits 0-9 154

1 in position 2 = 1 * 102

5 in position 1 = 5 * 10 4 in position 0 = 4 * 100 = 4 * 1

Hexadecimal (n=16) digits 0-9ABCDEF 3EA


E in position 1 = 14 * 16 A in position 0 = 10 * 1 in decimal 1002

Babylonian (base 60)

Binary Numbers

Binary (n = 2) digits 0 and 1

binary digit (bit) 1101



1 in position 0 = 1 * 1 in decimal 13

Why binary?

Switches the computer is a bunch of intricately-connected

switches transistors

a switch is either off or on Early computers were actually programmed

with switches early personal computers, too

An Early Home Computer

Memory

Usually described in terms of kilobytes (KB) or megabytes (MB) 1 byte = 8 bits 1 KB = 210 or 1024 bytes 1 MB = 220 or 1,048,576 bytes

256 MB of RAM 268,435,456 bytes or 2,147,483,648 bits more than 2 billion transistors

actually transistor / capacitor pair

16 million transistors in this L2 cache

Data Representation

Everything in the computer is binary the program the operating system HTML files the values manipulated by JavaScript

Part of what the computer does is translate from our representations to its representation = binary and back

Obvious Example

Images More about images later

Integers

Modern computers allocate 4 bytes (32 bits) to an integer 232 = 4.3 billion bit patterns but we need some for positive numbers and some

for negative Basic idea

give up one bit (highest-order) as a "sign" bit the problem

0000 0000 0000 0000 0000 0000 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000

Two's complement

Represent negative numbers in opposite order 1000 0000 0000 0000 0000 0000 0000 0000

-231 (not 2-31, typo in book) 1111 1111 1111 1111 1111 1111 1111 1111

-1

Integer representation

32 bits first bit = sign bit if sign bit = 0

interpret as binary number if sign bit = 1

flip all the other bits interpret as negative number

What is (231-1) + 1?

Floating point

Think of scientific notation 1234.56 convert so that the decimal point has one digit in

front of it 1.23456 x 103

since we know where the decimal point is three things to track

+ or – exponent of 10 value

Floating Point 32 bits

sign bit 8 bits exponent 23 bits fractional part

1234.56 sign bit = 0 exponent = 3 = 0000 0011 fraction = 123456 = 000 0001 1110 0010 0100 0000 0000 0001 1000 0001 1110 0010 0100 0000

Double-precision 64 bits 11 for exponent 52 for fraction more accuracy

Characters

Historically 1 byte (8 bits) = 1 character 8 bits = 256 possible bit patterns

Character set mapping between bit patterns and characters

A = 01000001 (65), a = 01100001 (97) does not work for languages with larger character sets

Unicode a character = 16 bits

65,536 characters

Characters

ASCII the most common mapping used today A-Z = 65-91, a-z = 97-113

Strings

Strings are lists (really arrays) of characters "foo" think of a list with 3 elements, each a character

Not 100% accurate see on Wednesday

Data Representation

Is determined by context what kind of variable is declared where the value came from

Example

Images

Complex topic actually Basic idea

divide the picture into an evenly-spaced grid picture elements = pixels

build a representation of the grid data turn into a file

To display reverse the process to create picture

Monochrome (B/W)

Each pixel 0 (on) or 1 (off)

Eight bit color

256 color palette associated with display 8 bit value indexes into palette

24-bit color

8 bits per color (RGB)

But

Consider a simple image 288 x 200 pixels = 57600 pixels 57600 x 3 bytes (24 bits) / pixel = 172, 800 bytes

At 3 K / sec 57 = 1 min

All useful image formats use compression

Image formats

Most common GIF JPEG PNG

How they differ use of color type of compression availability

GIF Format

Graphics Interchange Format .gif oldest uses repetitive pattern encoding

Pluses compression is accurate, no loss of quality

Minuses less compression possible image can only have 256 colors shading looks ugly

Applicability good for line drawings animation is supported

JPEG

Format Joint Photographic Experts Group .jpg average color values across pixels

Pluses Level of compression is adjustable Supports 24-bit color

Minuses Compression loses information

PNG

Format Portable Net Graphics .png developed in web era

Pluses has aspects of both GIF and JPG

Minuses older browsers don't support it

Bottom line

GIF line art unless there is continuous tone content

JPG images compression advantages of JPG not apparent below

200x200 or so can often get away with high compression

PNG consider using if your audience has the latest software

Rules of Thumb

Speed Dial-up about 5 K / sec DSL / Cable about 50 - 100 K / sec Don't make user wait more than 2-3 sec for

homepage Images deeper in site can be bigger

Note images are cached by browser won't be downloaded every time they appear

navigation bars, buttons, etc.

Wednesday

Strings Ch. 15

data representation robin burke it 130. outline data representation binary numbers image types

Documents