1. Data Encoding
COSC 1301

2. Computers and Data Computers store information as sequences of bits
Computers store many types of data:
numbers
text
audio
images
video

3. Standards
Look around – how many items do you see that are based on a standard?
Standards: make our lives simpler, more efficient
Sometimes there aren't any.

4. Not Much of a Standard But getting better

5. A Small Number of Standards
Imperial vs. metric

6. A Small Number of Standards
Candelabra vs Edisonhttp://

7. A Small Number of Standards
Candelabra vs Edison, , even when new things are introduced, they must conform.

8. Bitten by Lack of a Single Standard

9. Bitten by Lack of a Single Standard
Region codes intended to make it hard for things to be universal

10. Wishing for Standards http://www.sheldonbrown.com/tire-sizing.html
Go to this article to see how complicated the tire size situation is.
Image:

11. A General Trend Toward Standards
Word Sizes of Early Computers
EDVAC
44 bits
1947
MARK 1
40 bits
1948
EDSAC
17 bits
1949
CSIRAC
20 bits
UNIVAC I
12 digits
1951
IBM 701
36 bits
1952
CDC 1604
48 bits
1959
CDC 6600
60 bits
1964
IBM 360
32 bits
1965
x-86
16 bits
1978
x-32
1986
x-64
64 bits
2004
EDSAC had 18 bits but the first one wasn’t usable
CSIRAC – Australian
Word Size – natural unit of data for a particular processor
Word = fixed size group of bits that are handled as a unit by the hardware of the processor
Word size = number of bits in a word
Typically registers are word sized. The largest piece of data that can be transferred to and from memory in a single operation is a word. The largest address size (denoting a location in memory) is a word.
Modern processors: 8, 16, 32 or 64 bits. Minimum amount of storage given for any type of data is allocated in multiples of that word size.

12. Standard: Integer Representation
Representing integers in base 2: 93 1
Obvious how to represent integers

13. Integers 1 1 But what about: -93 sign bit
Representing integers in base 2: 93 1
But what about:
-93 1
Obvious how to represent integers
sign bit

14. Integers 1 But what about: -93 sign bit
sign bit
Problem: Two representations of zero – positive zero and negative zero
Unnecessary complexity
Better representations make it easier for the computer.
Obvious how to represent integers

15. Two's Complement: Negative Integers
Flip the bits: Then add 1: 1 1
Now addition and subtraction work.
You must tell me how many bits to use, and add leading 0s as needed. 1
A good explanation of why it works:

16. A Problem 104.23 10423 What should we do about:
If we always want two places after . : Then we could write:
10423
Sort of like counting cents instead of dollars. But we want a more general solution.
And then always treat it as though the decimal point were there.

17. Floating Point Numbers
Floating point representation: exponential/scientific notation
Example:
123l.45 can be represented as a decimal floating-point number with the integer as the significand and -2 as the exponent (and 10 as the base). It’s value is given by the following:
= X 10 -2
See the following slide to see how a computer stores this

18. IEEE Standard - Floating Point
Single Format:
32 bits (4 bytes) to store a floating point number:
1 bit for the sign
8 bits for the exponent
23 bits for the mantissa or significand
Double Format:
64 bits (8 bytes) to store a floating point number:
11 bits for the exponent
52 bits for the mantissa or significand

19. Text
To represent text digitally, need to be able to represent every possible character that may appear: Computers have revolutionized our world. コンピュータは私たちの世界に革命をもたらしました。 Les ordinateurs ont révolutionné notre monde.
English Japanese French

20. Text Decide how many characters we need to represent.
Then: determine the required number of bits.
English: 26 letters, 52 for upper and lower case. Plus punctuation...
And other languages?
character set: a list of characters and the codes used to represent each
Several character sets have been used over the years - a standard makes processing text easier

21. ASCII ASCII: American Standard Code for Information Interchange
1963: 7 bits per character = 128 different symbols
Thought to be enough at the time
8th bit in each character byte – used as a check bit or parity bit
check for errors in transmission of data
Later: Latin-1 Extended ASCII character set
All 8 bits used to represent character
Represent 256 characters – includes accented characters, other special characters

22. ASCII http://www.krisl.net/cgi-bin/ascbin.pl
Note that most of the control codes are obsolete now.

23. Representing Text Fourscore and seven … F o u r

24. Representing Text T h e n u m b e r i s 1 7 .
E D E
In hex

25. Computing with Text
Suppose we want to capitalize this entire paragraph:
Computers have revolutionized our world. They have changed the course of our daily lives, the way we do science, the way we entertain ourselves, the way that business is conducted, and the way we protect our security.
Let’s go back and look at the ASCII table to see how to do that.
Add Octal 40 to all the letters (but not the punctuation). Do it in Python with st.upper()

26. When We Need More Characters
What about things like:
简体字
Chinese string means “simple writing”.
ASCII not enough for international use.

27. When We Need More Characters
What about things like:
简体字
Answer: Unicode
Chinese string means “simple writing”
A conversion applet:

28. Unicode Previously, a letter maps to some bits:
A encoded as
In Unicode, a letter maps to a code point – a number like U+0639
U+ means Unicode
numbers are hexadecimal
Every character has a Unicode code point
This doesn't indicate how the code point is encoded as a sequence of bits, though
U+0041: English letter A
U+0639: Arabic letter Ain

29. Unicode Example: Hello
5 code points, one code point (i.e., number) per letter
U+0048 U+0065 U+006C U+006F
How is this stored in memory? Different standards for this.
One standard: UTF-8
Standard system for storing strings of Unicode code points in binary (i.e., U+DDDD stored in some number of bytes)

30. UTF-8
Code points stored in one byte
So English text looks same in UTF-8 as ASCII (backwards compatible)
Code points 128 and higher: 2, 3, up to 6 bytes
Hello: U+0048 U+0065 U+006C U+006C U+006F
Stored as: C 6C 6F (same as ASCII)
For Hebrew characters, accented letters, etc.: you may need more bytes