1. Dale & Lewis Chapter 3 Data Representation

2. Analog and digital information
The real world is continuous and finite, data on computers are finite  need to approximate real-world data for our computational needs
Analog data: information represented in a continuous form
Digital data: information represented in digital form

3. Analog and digital information

4. Noise in signals

5. Digitizing a signal Sample the signal in time within discrete levels
The pieces are numbered
The binary number system is used to represent the numbers
n bits can represent 2n numbers
Q: how many bits are needed to represent m numbers?
Actual number of bits that can be easily addressed in a computer sets some constraints

6. Representing text
English language character set: 26 letters (both upper and lower case), punctuation, numeric digits, etc
How many bits can we use?
What about other languages?

7. ASCII character set American Standard Code for Information Interchange
Each character is coded as a byte (8 bits)
7-bit code (1 check bit)
Later all 8 bits used in the “extended character set”
128 characters encoded (27)
95 visible characters
33 invisible (control) characters

8. 7-bit ASCII character set

9. ASCII Table The table above was sorted in decimal values
These decimal values are really representing binary sequences
So the character J is in position 74
This would be in Binary or 4A in Hexadecimal
j in 106 is in Binary or 6A in Hexadecimal
Notice anything? There is a purpose for that!
The Unicode character set
16-bit standard, 65,536 possible codes
Enough to cover the principal languages of the World
Superset of ASCII so the first 256 codes of Unicode are the same as Extended ASCII

10. Text compression Keyword encoding
Substitute frequently used words with single characters
i.e.: “as”  ^, “the”  ~, “and”  +, “that”  $, etc.
Problems:
These characters can’t be part of the text
Frequently used words tend to be short, so not much gain
Word variations are not handled: i.e. “The” vs. “the”

11. Run-length encoding
Replace long series of a repeated character with a special short code
i.e.: replace “AAAAAAA” with *A7
This is equivalent to with
Note that repetitions shorter than 4 characters are not worth encoding
Also note that the repetition number is encoded in binary, not ASCII, so that repetitions longer than 9 can be captured
Used in limited-palette image compression and fax machines

12. Huffman encoding Generalization of Morse Code
Morse code (dots & dashes) is based on distribution of letters in general English usage
Huffman encoding in based on distribution in a given message
Algorithm:
Encoding:
Build frequency table of letter usage
Build the code and encode the message
Decoding
Huffman code has the prefix property
Prefix property: no code is the front part of another code
Decoding processes the bit stream until a match
is found

13. Example of Huffman encoding/decoding
Message: DOORBELL
Encoding:
Compression ratio (vs ASCII): 25/64 = 0.39
Decode: