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

2. Announcements

3. Review
Discrete Symbol System
Digital Symbol System

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

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 another example

6. 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

7. 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

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

9. 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

10. 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

11. 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 …

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

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

19. 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

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

21. Random
Can you guess what this picture is?

22. 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

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

24. 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!!!

25. 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

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

27. 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

28. 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

29. 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

30. 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 * * * 1
= 3 * * * 1
= = 24510

31. 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