1. 1 COMS 161 Introduction to Computing Title: The Digital Domain Date: September 1, 2004 Lecture Number: 4

2. 2 Announcements Homework Assignment 2 Due on Friday Questions Comments Concerns Criticism Jokes

3. 3 Review Digital Domain Discrete Digital Analog (continuous) information

4. 4 Outline Analog (continuous) Information Digital information –Advantages –Disadvantages

5. 5 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 also continuous

6. 6 Analog information Amplitude, intensity, or volume Time Signal or waveform –Amplitude: how far up and down –Frequency: how many times per sec

7. 7 Frequency 1 second time

8. 8 Analog information Continuous –At every instant in time there is an amplitude –There is an infinite amount of information in an analog signal or waveform

9. 9 Discrete and finite –Amplitude is measured at distinct time intervals Digital information Time Amplitude, intensity, or volume

10. 10 –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 Digital information Time Amplitude

11. 11 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

12. 12 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 –…–…

13. 13 Digital advantages Electronic 1.Fast Operating speeds measured in billionths of a second 2.Precise Numbers are distinct and unambiguous –Precise manipulation (cloning) 3.Ordinal Ordered numbers –Simple alphabetical sorting

14. 14 Digital advantages 4.Efficient storage Practical to store large amounts of data in a small amount of area –iPod: 10,000 songs! How many CD’s would you need? 5.Fast Transfer Compare downloading a paper from the internet to: –Going to the library –Determining what you need is not there

15. 15 Digital advantages 6.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

16. 16 Digital advantages 7.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

17. 17 Digital advantages 8.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

18. 18 Digital advantages 8.Random Access(Cont.) Sequential access –Analog information –Must pass information that comes before what you wish to find 9.Selective Access Searched by content (selective) Find occurrences of a given word in a document

19. 19 Digital advantages 10.Compression Useful information is not totally redundant or totally random Redundant –Repeating Random –Nothing in common –TV snow –This lecture?

20. 20 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

21. 21 Redundant –Redundancy permits data compression Remove some of the redundancy Keep enough –Reconstruct the original exactly –Reconstruct a reasonable approximation of the original Example of compression –Repeat the following phrase nine times »COMS 161 is the best of the best classes at the H-S-C

22. 22 Random –Can you guess what this picture is?

23. 23 Digital advantages 11.Content Analysis and Synthesis Digital data can be processed, combined, and analyzed Ordered based on content Cookies –Allow web sites to taylor to you 12.Broad usefulness Many different forms of information can be represented this way

24. 24 Digital Domain Analog information –The natural form for many different types of information –Continuous in at least one dimension Digital information –Language of the computer –Analog information must be converted into a discrete (digital) form –Multimedia is all digital information

25. 25 Digital Domain Converting analog to digital information –We need a digital representation of the information –Recall, digital is a discrete system Where symbols are numbers The digital advantages –Therefore, we need a numerical encoding of the data Numerical means numbers

26. 26 Numbers Two types of notion used to represent 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

27. 27 Numbers –Positional notation Significance is given to order the digits appear in the number 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 »They use the same digits

28. 28 Positional notation 365 means –Three hundreds –Six tens –Five ones Each digit is multiplied by a power of 10

29. 29 Decimal number system Synonyms –Decimal number system –Decimal notation –Base-10 system Both digits and their location in the number are important Ten unique symbols (digits) –0, 1, 2, …, 9

30. 30 Octal number system Decimal is not the only positional number system available –Octal Positional,base-8 system Each digit is multiplied by a power of 8 Eight unique symbols (digits) –0, 1, 2, …, 7

31. 31 Binary number system –Binary Positional, base-2 system Each digit is multiplied by a power of 2 Two unique symbols (digits), 0 and 1

32. 32 Binary number system Digital and binary relationship –The language of computers use binary digits –Only 2 possible values 0 and 1 –Much simpler to make electronics that distinguish between one of two values Distinguishing between more than two values is very difficult

33. 33 Binary number system Since binary digits have two possible values Binary digits are called bits –They only contain a little “bit” of information –Numbers represented in binary form will (most likely) require more digits (bits) than the decimal form

34. 34 Binary number system To represent more information –Lump together multiple bits called strings One bit: 2 values Two bits:4 values (00, 01, 10, 11) Three bits: 8 values (000, 001, …, 111) Four bits:16 values (0000, …, 1111) Five bits:32 values Six bits:64 values Seven bits: 128 values Eight bits: 256 values

35. 35 Binary number system In general number of values = 2 number of bits –1 = 2 0 –2 = 2 1 –4 = 2 2 –8 = 2 3 –16 = 2 4 –32 = 2 5 –64 = 2 6 –128 = 2 7 –256 = 2 8

36. 36 Binary number system Common grouping –4 bits: nibble –8 bits: byte One byte represents 256 different values or items

37. 37 Binary number system –Letters in the English language A = 65 10 = 0100 0001 2 B = 66 10 = 0100 0010 2 … Z = 90 10 = 0101 1010 2 … a = 97 10 = 0110 0001 2 … Z = 122 10 = 0111 1010 2 Numbers are still left over for punctuation

38. 38 Binary number system Precision –The number of bits used to represent an item Letter: precision of 8 bits Integer (whole number): precision of 32 or 64 bits –Always finite Computers have finite precision –Presents some limitations

39. 39 Hexadecimal number system Sometimes called hex –Positional,base-16 system –Each digit is multiplied by a power of 16 –Sixteen unique symbols (digits) 0, 1, 2, …, 15 Symbol a or A for 10 Symbol b or B for 11 Symbol e or E for 14 Symbol c or C for 12 Symbol f or F for 15 Symbol d or D for 13

40. 40 Hexadecimal number system A hex number can represent 16 different items –Equivalent to 4 bits –Makes it easy to convert between binary and hex Group bits by 4’s from the left end Substitute the hex symbol –90 10 = 0101 1010 2 = 5A 16 »Is the base 16 really needed? –66 10 = 0100 0010 2 = 42 16

41. 41 Hexadecimal number system Use the backwards conversion to convert hex to binary –One hex digit is equivalent to 4 bits –Substitute the binary nibble Always start at the right end Add zeros to the left end as necessary to fill in 4 bits

42. 42 Hexadecimal number system HEXDECBIN 000000 110001 220010 330011 440100 550101 660110 770111 881000 991001 A101010 B111011 C121100 D131101 E141110 F151111

43. 43 Digitization The process of converting analog information into binary –Discrete forms are unambiguous Text and numbers are discrete –Conversion of discrete to digital Come up with a mapping –As we did with the letters

44. 44 Binary Coded Decimal Integers (whole numbers) –One mapping is to use its binary equivalent Binary Coded Decimal (BCD) –0 10 = 0000 2 –1 10 = 0001 2 – … –9 10 = 1001 2 Need a minimum of 4 bits to represent 10 different values –Some 4 bit quantities are wasted

45. 45 Binary Coded Decimal String of decimal digits –Each decimal digit is represented by 4 bits –The number of bits needed to represent different numbers vary –Performing arithmetic is complicated