COMS 161 Introduction to Computing Title: The Digital Domain Date: January 19, 2005 Lecture Number: 4

Announcements

Review Discrete Symbol System Digital Symbol System

Outline Analog (continuous) information Digital information Advantages Disadvantages

Analog Information Natural form of representing information Sound is analog information Continuous over some dimension(s) Time is a natural dimension for sound Sound is composed of variations in air pressure A pressure measurement can be made at any and all times during the sound Temperature is another example

Analog information Signal or waveform Amplitude: how far up and down intensity, or volume Time Signal or waveform Amplitude: how far up and down Frequency: how many times per sec

Analog information Continuous At every instant in time there is an amplitude There is a value The number line is continuous Always another number between two given numbers There is an infinite amount of information in an analog signal or waveform

Digital information Discrete and finite Amplitude is measured at distinct time intervals Time Amplitude, intensity, or volume

Digital information Finite sequence of instantaneous pulses, which we call samples Finite sequence We can count and label the samples Instantaneous pulses The amplitude, intensity, or volume at one specific instant in time Time Amplitude

Digital information No measurements are made between the instantaneous pulses (samples) Digital representations contain a finite amount of information Digital information Not exact as analog More precise (repeatable) More compact

Digital information The number of samples is fundamentally important when accurately representing an analog signal Appropriate sampling allows digital information to replace analog information For example CD’s, MP3’s, DVD’s Digital telephones …

Digital advantages Electronic Fast Precise Ordinal Operating speeds measured in billionths of a second Precise Numbers are distinct and unambiguous Precise manipulation (cloning) Ordinal Ordered numbers Simple alphabetical sorting

Digital advantages Efficient storage Fast Transfer Practical to store large amounts of data in a small amount of area iPod: 10,000 songs! How many CD’s would you need? Fast Transfer Compare downloading a paper from the internet to: Going to the library Determining what you need is not there

Digital advantages Absolute replication Cloning No loss or degradation of information when making a copy Copies of downloaded papers are just as clear as the original Photocopying adds noise and loses information in the process Copies of copies become unintelligible Music for prosperity Compare to my old LP’s

Digital advantages Resolution independence Resolution: amount of detail Higher resolution means more detail and therefore higher fidelity Downloaded information can be scaled to match you system Either higher or lower resolution Music is resampled to match the resolution of your system Resolution is machine independent

Digital advantages Random Access Direct access to digital data, provided we know where to look for it Random access All accesses take the same amount of time (latency) regardless of where the data resides

Digital advantages Random Access (Cont.) Selective Access Sequential access Analog information Must pass information that comes before what you wish to find Selective Access Searched by content (selective) Find occurrences of a given word in a document

Digital advantages Compression Useful information is not totally redundant or totally random Redundant Repeating phrase Random Nothing in common TV snow This lecture?

Redundant How many times does this message have to be transmitted, heard, or seen before it is not necessary to continue COMS 161 is the best of the best classes at the H-S-C

Redundant Redundancy allows for data compression Remove some of the redundancy Keep enough Reconstruct the original Reasonable approximation of the original

Random Can you guess what this picture is?

Digital advantages Content Analysis and Synthesis Broad usefulness Digital data can be processed, combined, and analyzed Ordered based on content Cookies Allow web sites to taylor to you Broad usefulness Many different forms of information can be represented this way

Bits and Bytes Digital representation of information Numerical encoding Let’s talk about numbers

Numbers Non-positional notation No special significance is given to order Counting numbers on your fingers Tick mark counting method The number of items is important, not the order My honey do list Not important which task I do first, just so I get them all done NOW!!!

Numbers Positional notation Significance is given to order the digits in the number appears The decimal numbering system uses positional notation This is the system we use 365 is not the same a 653 These are completely different numbers but they use the same digits

Positional notation Three hundred, sixty five means Three hundreds Six tens Five ones 365 365 = 3 hundreds + 6 tens + 5 ones

Positional notation In positional notation Each successive digit to the left is multiplied by an increased power of 10 365 100 = 1 104 = 10,000 101 = 10 105 = 100,000 102 = 10*10 =100 106 = 1,000,000 103 = 10*10*10 = 1,000 107 = 10,000,000

Decimal number system Synonyms Decimal notation Base-10 system Both digits and their location in the number are important Ten unique symbols 0, 1, 2, …, 9

Octal number system Decimal is not the only positional number system available Octal Base-8 system Each digit is multiplied by a power of 8 Eight unique symbols 0, 1, 2, …, 7

Octal number system = 3 * 8 * 8 + 6 * 8 + 5 * 1 To convert an octal number into a decimal number Just do the math!! = 3 * 8 * 8 + 6 * 8 + 5 * 1 = 3 * 64 + 6 * 8 + 5 * 1 = 192 + 48 + 5 = 24510

Octal number system Counting in octal 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17 20, 21, 22, 23, 24, 25, 26, 27 … 70, 71, 72, 73, 74, 75, 76, 77 800, 801, 802, 803, 804, 805, 806, 807