Too much information running through my brain.

We live in the information age. Knowledge comes from careful investigation of information. Information is represented/encoded as data. – What information is represented by an abacus? How? – What information is represented on a DVD? How? – What information is encoded on a credit card? How? DATA: The quantities, characters, or symbols on which operations are performed by a computer.

How can a picture or a sound or a temperature reading become data? Data comes in two types: – Continuous: infinitely variable points – Discrete: finite number of points/choices

How long might it take a light bulb to burn out? What was your ACT score? How tall are you? How many books did you read this year? How much water did you drink this week? How many gen-ed courses have you taken at UW-L?

In electronics, signals are known as either – analog (meaning a continuous signal) – digital (meaning a discrete signal)

Information needs to be encoded in such a way as to be processed. – Electrical signals can be processed. – Even analog signals can be processed, but digital is simpler. In computers, there are two discrete (digital) signals: on and off. It's easy to tell if an electrical signal is on or off: – Electric fence – Electric socket – Light bulb

Bit: short for "binary digit". A bit is the representation used for the smallest (atomic) amount of computer data. – A bit is either ON or OFF. – You can think of a bit as an extremely small battery that can be quickly charged and discharged. When charged, the bit is ON. When discharged, the bit is OFF. This is essentially what a single transistor is. – Mathematically speaking, a bit is usually understood as the value 0 when OFF and the value 1 when ON. – Since there are only two values, a bit is known as a 'binary' digit. 0 1

What if you had two bits in a sequence. How many different patterns (sequences) could there be?

What if you had three bits in a sequence. How many different patterns (sequences) could there be?

What if you had four bits in a sequence. How many patterns could there be? What if you had N bits in a sequence. How many patterns could there be? With more bits you can store more information. – One more bit doubles the amount. # Bits# of Patterns N2N2N

One bit is too small to use as a measurement. – Nobody says: "I've got a 10 GigaBit IPod" Measures of data capacity are based on a byte. – 1 byte = 8 bits – 1 bytes can have 256 different patterns – 1 byte is big enough to represent many kinds of things PrefixSymbolBase 2Decimal KilobyteK2 10 1,024 MegabyteM2 20 1,048,576 GigabyteG2 30 ≈1,000,000,000 TerabyteT2 40 ≈1,000,000,000,000 PetabyteP2 50 ≈1,000,000,000,000,000

A string of bits can represent various things The length of a bit string controls the number of things that can be represented What is the shortest bit string for representing 100 different special symbols?

How much data capacity do you need to encode: – The complete works of William Shakespeare? – One 4 minute pop song (MP3)? – One digital picture (JPEG)? – One feature length movie (DVD)? – All of Wikipedia (As of Jan 2010)? – The entire U.S. Library of Congress (As of Apr 2011)?

All digital data is a sequence of bits. How can we represent an integer number as a sequence of bits? Consider the decimal number 515. – A sequence of digits – Digits are one of: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 – Meaning of a digit depends on position: power of 10 – 515 = 5× × ×10 0 Consider the binary number 101. – Binary uses a base-2 (or radix 10) system rather than base 10 – Digits are one of: 0, 1 – Meaning of a digit depends on position: power of 2 – 101 = 1× × ×2 0

= – 1× × × × × ×2 0 – 1×32 + 0×16 + 1×8 + 1×4 + 1×2 + 0×1 – – = – 1× × × × × ×2 0 – 1×32 + 1×16 + 0×8 + 0×4 + 0×2 + 1×1 – – 49

It's easy to get confused and not be sure of what base a number is written in. For example, is 111: – One hundred eleven? – Five? A subscript can be used to specify the base whenever it is unclear. – is equal to five – is equal to one hundred eleven.

What is the biggest number you can have with – Two bits? – Three bits? – Four bits? – Five bits? – N bits?

While we can represent an integer as a sequence of bits, is it possible to represent a real number such as 2.31 or 2.125? In base 10, the value means: – 2× × × ×10 -3 In base 2, the value means: – 1× × × ×2 -3 – 1×1 + 1×(1/2) + 0×(1/4) + 1×(1/8) – – 1.625

Consider the value 1/3. How many decimal digits does it take to accurately represent as a real number? – 1/3 = Consider the value 1/5. How many decimal digits does it take to accurately represent as a real number? How many binary digits? – 1/5 = – 1/5 = Since it requires a potentially infinite amount of bits to store a real number, computers can be imprecise.

Can text be represented as a sequence of binary digits (bits)? Text is a made of pictures (also known as symbols or characters). Each character can be associated with an integer number CharacterDecimalBinary A B C D E F ……… Z

The numbers associated with a character can obviously be stored About how many unique numbers are required for English text? (asked another way, how many unique characters did William Shakespeare ever use?) – One byte has enough capacity to store an English character. About how many unique numbers are required for Chinese text? – Two bytes is enough for most languages: 电脑

Most computers that are configured for English writers, use the ASCII table. This table associates numbers with English text.

How might a computer store a 'color'? What are the primary colors of pigment? – Cyan, magenta, yellow What are the primary colors of light? – Red, green, blue

RGB color model – Uses red, green, and blue as the primary colors. – Any color can be represented by combining different amounts of these three primaries. Consider a flashlight that has a slider that chooses the strength of light emitted. – Setting the slider to zero, the flashlight is turned completely off – Setting the slider to 255, the flashlight generates as much light as it is capable of generating. Consider three such flashlights – Each light emits purely red; green; or blue light. If all three flashlights are aimed at the same spot on a white wall any color can be projected onto the wall by adjusting the slider values on the three lights in different ways.

Could you encode an image as a sequence of bits? – Starting from the upper-left pixel, scan the image left-to-right, top-to-bottom – Record each pixel that you encounter. How many bits would be required for a – 100x100 image? – 1024x768 image? Most JPG files of 1024x768 are about 3-4 Meg. How?

There are many different ways to encode the same information. Some ways use more bits than others. Consider a black & white 8x8 image. – Use 0 for white and 1 for black – This is known as 'raw' or 'bitmap' format

Run length encoding is another way to encode images – A 'run' is the length of successive like-colored pixels – Store the lengths of these runs for each row, starting with white ,4,2 1,1,4,1,1 1,1,1,2,1,1,1 1,6,1 1,1,1,2,1,1,1 1,2,2,2,1 1,1,4,1,1 2,4,2 Raw Run Length Can you think of numbers in the Run Length code above that are not needed?

Consider another way to store images. 1, 5, 2 1, 1, 4, 1, 1 1, 5, 2 1, 1, 2, 1, 3 1, 1, 3, 1, 2 1, 4, 1, 1 8 a total of ____ numbers Raw pixels Run Length Encoding a total of _____ numbers compression - a way to represent data in more compact form

When data is compressed, information is encoded using fewer bits. – This speeds transmission – Reduces storage cost (smaller drives) – May increase processing (must un-compress to view/process) For pictures, there are two types: – Lossless: No information is lost – Lossy: Information may be lost