Encoding Things for Computers Section 17.1 Chapter 3
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Watson http://www.youtube.com/watch?v=WFR3lOm_xhE
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Digital vs Analog Digital is to analog as steps are to
ramps.
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Digital vs Analog.
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.
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Standards A very old idea. Sometimes there arent any. But
theyre very common. And theres a general trend in the direction of
standards.
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A Very Old Idea Along the Danube River
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No Standards
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Not Much of a Standard
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Some Common Standards
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A Small Number of Standards
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Bitten by Lack of a Single Standard
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Wishing for Standards
http://www.sheldonbrown.com/tire-sizing.html
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A General Trend Toward Standards Word Sizes of Early Computers
EDVAC44 bits1947 MARK 140 bits1948 EDSAC17 bits1949 CSIRAC20
bits1949 UNIVAC I12 digits1951 IBM 70136 bits1952 CDC 160448
bits1959 CDC 660060 bits1964 IBM 36032 bits1965 x-8616 bits1978
x-3232 bits1986 x-6464 bits2004
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Integers 1040 1 1 0 1 0 0 0 The first step is obvious:
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What About Long Integers? n! : if n = 1 then 1 else n * (n-1)!
def factorial(n): result = 1 for j in range(1,n+1): result = result
* j return (result)
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Integers 1040 1 1 0 1 0 0 0 The first step was obvious: But
what about this: -104 1 1 1 0 1 0 0 0 sign bit
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Two Problems sign bit -1041 1 1 0 1 0 0 0 Two representations
of 0: Adder and subtractor have to check sign bit and branch
accordingly. The best representation: Should make things easy for
the computer. Since people dont matter: well never see it.
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Twos Complement 104 0 1 1 0 1 0 0 0 -104: 1 0 0 1 0 1 1 1 Flip
the bits: Add 1: 1 0 0 1 1 0 0 0 A good explanation of why it
works:
http://www.cs.cornell.edu/~tomf/notes/cps104/twoscomp.html
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But What Happens Now? 11011001 + 11100101
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But What Happens Now? 11011001 + 11100101 Overflow, if we stick
with a fixed-length word (which Python doesnt do)
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Another Problem 104.23 What should we do about:
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Another Problem 104.23 What should we do about: If we always
want two places after. : Then we could write: 10423 And then always
treat it as though the decimal point were there.
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Floating Point Well do it in decimal: NumberFloating Point
4.324.32e0
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Floating Point Well do it in decimal: NumberFloating Point
4.324.32e0 456.24.56e+2 Multiply by 10 2
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Floating Point Well do it in decimal: NumberFloating Point
4.324.32e0 456.24.56e+2.00044.0e-4 Multiply by 10 -4
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Floating Point Well do it in decimal: NumberFloating Point
4.324.32e0 456.24.56e+2.00044.0e-4
56784657846352*345262511960561349752268586352 Note: Python will
create very large integers.
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Floating Point Well do it in decimal: NumberFloating Point
4.324.32e0 456.24.56e+2.00044.0e-4
56784657846352*345262511960561349752268586352
1960561349752268586352/29.802806748761343e+20
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Rounding Error >>> 156738*.028 4388.664 >>>
int(_) 4388 >>> Where did the.664 cents go? We can force
Python to round instead of truncate. Our balance is $1,567.38 and
the interest rate is 2.8%:
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Rounding Error But what about this: Our balance is $1,567.38
and the interest rate is 2.8%: >>> 156738*.028 4388.664
>>> int(_ +.5) 4389 >>> >>> 166730*.05
8336.5 >>>
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Salami Slicing
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Text 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.
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Text 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. Les ordinateurs ont rvolutionn notre
monde. Ils ont chang le cours de notre vie quotidienne, notre faon
de faire la science, la faon dont nous nous divertissons, la faon
dont les affaires sont menes, et la faon dont nous protgeons notre
scurit.
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Text 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. Les ordinateurs ont rvolutionn notre
monde. Ils ont chang le cours de notre vie quotidienne, notre faon
de faire la science, la faon dont nous nous divertissons, la faon
dont les affaires sont menes, et la faon dont nous protgeons notre
scurit.
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Representing Text Decide how many characters we need to
represent. Determine the required number of bits. ASCII: 7 bits.
Can encode 2 7 = 128 different symbols. At the time (1963), it was
felt that this was enough. Much concern about data transmission
speed. The 8 th bit, if available, could be used for a parity
bit.
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ASCII http://www.krisl.net/cgi-bin/ascbin.pl
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Representing Text Fourscore and seven F o u r 01000110 01101111
01110101 01110010
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Representing Text T h e n u m b e r i s 1 7. 54 68 65 20 6E 75
6D 62 65 72 20 69 73 20 31 37 2E
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Computing with Text 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. Suppose we want to
capitalize this entire paragraph: Lets go back and look at the
ASCII table to see how to do that.
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Computing with Text in Python chr(65) ord('A') ord('A') + 32 st
= chr(_) mystuff = 'Now is the time ') mystuff.upper()
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When We Need More Characters What about things like:
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When We Need More Characters What about things like: Answer:
Unicode A conversion applet:
http://www.pinyin.info/tools/converter/chars2uninumbers.html
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Unicode Unicode lists 1,114,112 code points in the range: 0 16
to 10FFFF 16 divided into seventeen planes: the basic multilingual
plane, and 16 supplementary planes), each with 65,536 (= 2 16 )
code points. http://www.unicode.org/charts/
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Unicode There exist different ways of mapping those 1,114,112
code points to specific byte patterns. In December, 2007 UTF-8
surpassed Ascii on the Web. Watch them stream by:
http://www.babelstone.co.uk/Unicode/unicode.html
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Saving Space Key idea: Common things should be short. Natural
languages evolve to do this. Examples:
http://www.paulnoll.com/Books/Clear-English/English-3000-common-words.html
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Saving Space Key idea: Common things should be short. Samuel
Morse:
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Saving Space Key idea: Common things should be short. Huffman
coding:
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Saving Space Key idea: Common things should be short. UTF-8
encoding of Unicode http://en.wikipedia.org/wiki/UTF-8
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But What Do Symbols Look Like? Computers have revolutionized
our world.
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The Basic Idea results = google(text, query)
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The Basic Idea results = google(text, query) if
word_count(text) > 5000: return(Done!!) else: return(No sleep
yet.)
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The Basic Idea results = google(text, query) if
word_count(text) > 5000: return(Done!!) else: return(No sleep
yet. display = render(text, font)
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Pixel Based Fonts
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TrueType Fonts Each symbol is represented as a set of lines and
Bzier curves: Then code associated with each display device turns
the description into pixels or rasters as necessary. So a font is
just another file of bits.
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The First Part of the Arial TrueType Font File
???????pDSIG$=???|GDEF^#]r?u???GSUB?u?? JSTFm*i?l???LTSHe
C?t???6VDMXPj??#??cmap @j:????jcvt *v??
??0fpgmyY??0??ngasp???t???glyf??bhdmx
??4??(head&??|???6hhea3?????$hmtx4X@??P??(kern7a96?`??`locaai2????,maxp
G????? namee;??? post~?2??AprepR?? ?? ??????_
N?C?&???????????????????????v? ???/?V?? ??????3??3???f
??z??????????Mono?@? Q3 >@???????????9??9??9??^s?s?I
?wV?X?Z?|?|?@?r9??A9?9??s?Us?s?
