CS73N Meeting 09 Notes: Representation 7 Feb 03
By Gio Wiederhold, Updated 28 Jan 2001.
Topics Covered briefly
For computers to deal with data, there has to be a mapping from what people underrstand to bits.
Bits are zero/one switches - as a row of light switches giving a postive or zero voltage, or the direction of magnetization of the magnetic cores in the exhibit, or a cell in a chip set up so that if a voltage is given as input either no or a postive voltage is returned.
But what those bits mean depends on the cosen representation.
Representations
For numbers: unary, binary, decimal:
- unary: like counting on your fingers: 10 fingers for 0 to 9 (that's how the class notes start too)
- binary: using the position as an exponent in the (binary) number system: 10 fingers 0 to 1023!
- decimal: using groups of 4 bits to represent 0 to 9, and optionally {. , + - space null }
- characters (ASCII): using goups of 7 bits to represent 95 graphic characters as digits and common letters, 16 control characters. as new-line, tab,end-of-message ,bel, etc, and null.
- characters {bytes}: using goups of 8 bits to represent ASCII nad 256 more charcaters for many common languages. mathematics, and some special purposes --not well standardized see [Note HTML]
- small numbers: use of goups of 16 bits to represent numbers from -32768 to +32767
- Unicode: using goups of 16 bits to represent all of the worlds characters - some ideographs require composition of two unicode characters
- bigger numbers: 32-bits to represent integers
- floating point numbers: often 24 bits to represent a fraction, 7 bits to represent an exponent,and 1 bit for a sign. Some use base-2 exponents, and some base-16 exponents for more range, less precision (21 bits effectively)
- double-precision floating point numbers: 64 bits with a fraction, exponent, and sign
MORE ON NUMBERS
Number representation -- decimal vs, binary
Counting with only two symbols {0, 1} . (need a reference to reading?).
Why Binary numbers?
What is the benefit of Binary Number representation: reliability through simplicity.
Counting with only two symbols {0, 1} .
What about 10 {0, .. , 9}?
What about 3 {-1,0,+1}?
Other base systems: 10, 3,
...
Character sets: ASCII 7 bits = 128 characters - 33 for control. (32 + null) Derived from teletypes. Leaves 95 printable characters
In practice 8 bits = 256 choices, ASCII plus whatever someone wants.
For more extensive languages there is Uniciode 16 bits 64K choices (1K is 1024 -- why)
Text
Build characters to words or numbers; words or numbers to records or sentences; records or sentences to messages; messages to papers or books; papers or books to knowledge?
Dates
Many formats. Easily ambiguous. Y2K problem.
Able to compute with dates? integer - integer Data - date
Use letters for months in international communication! Nearly the same amount of space .
Origin of names of months.
Anything on the web is international.
Figures:
Bit Image: Encodings of 2D graphics as height x width pixels -- each pixel has 3 x intensity of color (RGB) or (Luminosity, .. ) A variety of standards, GIF, BMP, JPEG (why)
Vector: collection of lines defined by endpoints (x,y) for 2D, (x,y,z) for 3D.
For viewing 3D representation has to be converted to 2D, b y software or hardware [SGI -- Jim Clark's first company] What about 3D bit images? What about movies?
Representation Character set:
Complexity of representation for human comprehension:
George Miller: The Magical Number 7 ± 2 Structure:
linear (DNA) ; Language, logical sequential reasoning parallel processing: many units doing the same thing (easy to program) SETI@home, protein folding at home , harder if partitions are diverse hierarchical - divide and conquer - from one viewpoint networks: intersecting hierarchies Example Bill-of-Materials Processing BOMP Parts per supplier, parts for assembly of space shuttle 2D: images, memory, pattern matching, 2.5D: Stereo ; multiple angles, focus, Polaroid glasses 3D: folded protein, real-world objects, engineering models, holograms for visualization
Distributed, autonomous development of standard protocols.
For ARPAnet and continuing: Requests for comments (RFCs) to proposals, collected at SRI International. Implemented and adopted by the community, after discussion, when effective.
Example: SMTP (RFC 8xx): combined messy Telnet and FTP operations into a simple email protocol.
Alternate means of developing standards
Implement, show, convince others of usefulness and leverage if major company (now Microsoft, formerly IBM)
Committee of wise men, supported government mandates. Governments can set standards, but are rarely competent to do so. Politicians and marketers think it's simple, like electric plugs.
Commercial value of getting one's standard accepted. Standards are a major commercial competitive weapon.
Now we have a surfeit of standards (look at video storage), confusion, cost, dirty tricks.
Standards take long to develop, criticize, implement, get the bugs ou
Then they stick around for a long time, often too long.
Two-horse Roman chariot -> grooves in limestone street --> all carts --> mines --> steam-propelled mine carts -> RRs -> BART.
The various protocols communication differ in terms of
- Security
- Suitability for business
- Cost reimbursement.
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