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- しじん やぶき
- 5 years ago
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Transcription
1 2
2 Outline
3 Digital information world
4 2.1 Bit & information amount
5 2.1.1 Bit binary digit n 2 n ) 26 5 (16<26<32)
6 2.1.2 Bit & Byte
7
8 2.1.3 Information amount (Information theory) 1948 A mathematical theory of communication (1) (2) (3) E. Claude Elwood Shannon
9 entropy H H = n i= 1 Information amount p i log 2 p i 1/ H = log2 log2 = ( 1) ( 1) = /6 A 5/6 B 1 A 5 B H = log2 log2 = ( 2.58) ( 0.26) =
10 2.1.4 (1)
11 2.1.4 (2)
12
13
14
15 2.1.4
16 2.1.4
17 2.1.5 compression encode decode
18 2.1.5 compression
19
20
21
22 2.1.5 XVL CAE XVL extensible Virtual world description Language 3D
23 2.1.5 XVL CAE XVL Web3D XVL Web Master
24 2.1.5 XVL CAE XVL XML D SVG
25 2.1.5 XVL CAE XVL Web Master
26
27 2.2.1 binary system) 10 decimal system) 16 hexadecimal system)
28 yes or no 10
29 2.2.3
30 2.2.4 complement
31 2.2.5 floating point) a = m 2 e (exponent) (mantissa) (base)
32
33 2.3.1 reliability
34 2.3.2 parity check) 1 ( ) ( )
35 2.3.2 parity check)
36 2.3.2 parity check)
37 2.3.3 Error correction Hamming code) ( ) 1950 Hamming ( ) RAID-2
38 2.3.3 Hamming distance) n 2 (0,1) X,Y d(x,y) = (x i y i ) X = x 1 x 2 x n (x i =0,1) Y = y 1 y 2 y n (y i =0,1) 0 0=0 0 1=1 1 0=1 1 1= ,001,010,100,101,110,
39 2.3.3 Hamming code) (a, b, c, d) (e, f, g) e = b c d f = a c d g = a b d (1) a, b, c, d, e, f, g) a b c d e f g
40 s1 s2 s a b c d e f g Hamming code) s1 = d e f g s2 = b c f g s3 = a c e g 0 = d e f g 0 = b c f g 0 = a c e g e,f,g e,f,g (2)+(3) f+f=0, g+g=0 e 0=d+e+f+g+b+c+f+g 0=b+c+d+e+f+f+g+g 0=b+c+d+e e=b+c+d (2) (3) (4) e = b c d f = a c d g = a b d
41 2.3.3 Hamming code) y n y = + n = (a+ n1, b+ n2, g+ n7) s1 =(d+n4)+(e+n5)+(f+n6)+(g+n7) = (d+e+f+g)+(n4+n5+n6+n7)= n4+n5+n6+n7 s2 = (b+n2)+(c+n3)+(f+n6)+(g+n7) = (b+c+f+g)+(n2+n3+n6+n7)= n2+n3+n6+n7 s3 = (a+n1)+(c+n3)+(e+n5)+(g+n7) = (a+c+e+g)+(n1+n3+n5+n7)= n1+n3+n5+n7
42 2.3.3 Hamming code) n1 n2 n3 n4 n5 n6 n7 s1 s2 s
43 2.3.3 Hamming code) S1=0 S2=0 S3=1 s1 = d e f g s2 = b c f g s3 = a c e g a b c d e f g
44
ohp1.dvi
2008 1 2008.10.10 1 ( 2 ) ( ) ( ) 1 2 1.5 3 2 ( ) 50:50 Ruby ( ) Ruby http://www.ruby-lang.org/ja/ Windows Windows 3 Web Web http://lecture.ecc.u-tokyo.ac.jp/~kuno/is08/ / ( / ) / @@@ ( 3 ) @@@ :!! ( )
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~ ~ NO YES ~ ( NO YES ) YES NO NO YES ~ ( NO YES ) YES NO 1 1 NO 2 NO 2YES YES 1 (1) 25 26 2 3 () () () () 4 () () 5 6 () 7 () 8 9 1-3-1 10 3 11 12 ~1. (1) () () (2) (3) () (4) () () (5) (6) (7) (1) (2)
del.dvi
(2013, c ) http://istksckwanseiacjp/ ishiura/lc/ 1 2, 8, 16 2 10 (2 ) 11 2, 8, 16 10 (decimal) 1192 10 = 1 10 3 + 1 10 2 + 9 10 1 + 2 10 0 (a n 1 a n 2 a 1 a 0 ) 10 = 8 (octal) n 1 i=0 a i 10 i 710 8 =
..0.._0807...e.qxp
4 6 0 4 6 0 4 6 8 30 34 36 38 40 4 44 46 8 8 3 3 5 4 6 7 3 4 6 7 5 9 8 3 4 0 3 3 4 3 5 3 4 4 3 4 7 6 3 9 8 Check 3 4 6 5 3 4 0 3 5 3 3 4 4 7 3 3 4 6 9 3 3 4 8 3 3 3 4 30 33 3 Check Check Check Check 35
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P03 P05 P10 P13 P18 P21 1 2 Q A Q A Q A Q A Q A 3 1 check 2 1 2-1 2-2 2-3 2-4 2-5 2-5-1 2-6 2-6-1 2-6-2 2-6-3 3 3-1 3-2 3-3 3-4 3 check 4 5 3-5 3-6 3-7 3-8 3-9 4-1 4-1-1 4-2 4-3 4-4 4-5 4-6 5-1 5-2 4
1 2 3 4 1 2 1 2 3 4 5 6 7 8 9 10 11 27 29 32 33 1 2 3 7 9 11 13 15 17 19 21 23 26 CHECK! 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
one way two way (talk back) (... ) C.E.Shannon 1948 A Mathematical theory of communication. 1 ( ) 0 ( ) 1
1 1.1 1.2 one way two way (talk back) (... ) 1.3 0 C.E.Shannon 1948 A Mathematical theory of communication. 1 ( ) 0 ( ) 1 ( (coding theory)) 2 2.1 (convolution code) (block code), 3 3.1 Q q Q n Q n 1 Q
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20 7 1 22 7 1 1 2 3 7 8 9 10 11 13 14 15 17 18 19 21 22 - 1 - - 2 - - 3 - - 4 - 50 200 50 200-5 - 50 200 50 200 50 200 - 6 - - 7 - () - 8 - (XY) - 9 - 112-10 - - 11 - - 12 - - 13 - - 14 - - 15 - - 16 -
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19 1 19 19 3 8 1 19 1 61 2 479 1965 64 1237 148 1272 58 183 X 1 X 2 12 2 15 A B 5 18 B 29 X 1 12 10 31 A 1 58 Y B 14 1 25 3 31 1 5 5 15 Y B 1 232 Y B 1 4235 14 11 8 5350 2409 X 1 15 10 10 B Y Y 2 X 1 X
情報理論 第5回 情報量とエントロピー
5 () ( ) ( ) ( ) p(a) a I(a) p(a) p(a) I(a) p(a) I(a) (2) (self information) p(a) = I(a) = 0 I(a) = 0 I(a) a I(a) = log 2 p(a) = log 2 p(a) bit 2 (log 2 ) (3) I(a) 7 6 5 4 3 2 0 0.5 p(a) p(a) = /2 I(a)
2
2007 8 12 1 Q&A Q1 A 2007 6 29 2008 1 1 14 1 12 1 2 3 1 1 13 1 2 15 1 1 2 Q2 A 627 1 20 1 1 3 15 2003 18 2 3 4 5 3 406 44 2 1997 7 16 5 1 1 15 4 52 1 31 268 17 5 60 55 50 1999 3 9 1999 3 39 40 44 100 1
1 2 3 4 5 1 1 136 2 137 2 1 1 138 2 1 2 139 140 141 142 3 143 3 144 145 4 1 2 146 3 4 147 5 1 2 3 148 1 2 149 3 5 1 2 150 3 151 1 152 2 153 6 1 2 154 3 155 4 1 156 2 3 4 5 157 7 1 2 3 4 158 5 159 6 8 1
2007.3„”76“ƒ
76 19 27 19 27 76 76 19 27 19 27 76 76 19 27 19 27 76 76 19 27 19 27 76 1,27, 2, 88, 8,658 27, 2,5 11,271,158 1,712,876 21,984,34 1,, 6, 7, 2, 1,78, 1,712,876 21,492,876 27, 4, 18, 11,342 27, 2,5 491,158
1631 70
70 1631 1631 70 70 1631 1631 70 70 1631 1631 70 70 1631 1631 70 70 1631 1631 70 70 1631 9,873,500 9,200,000 673,500 2,099,640 2,116,000 16,360 45,370 200,000 154,630 1,000,000 1,000,000 0 648,851 730,000
72 1731 1731 72 72 1731 1731 72 72 1731 1731 72 72 1731 1731 72 72 1731 1731 72 12,47,395 4, 735,5 1,744 4,5 97, 12,962,139 6,591,987 19,554,126 9,2, 4, 7, 2, 9,96, 6,591,987 16,551,987 2,847,395 35,5
() DTD
20 5 () 1...1 2...2 3...5 3-1...5 3-2...11 4...13 5...15 5-1...15 5-2...15 6...16 7...18 7-1...18 7-2...19 7-3...20 8...21 8-1...21 8-2...22 8-3...23 1 DTD... 1-1 2 XML... 2-1 3... 3-1 4 XML... 4-1 ()
p01.qxd
2 s 1 1 2 6 2 POINT 23 23 32 15 3 4 s 1 3 2 4 6 2 7003800 1600 1200 45 5 3 11 POINT 2 7003800 7 11 7003800 8 12 9 10 POINT 2003 5 s 45700 3800 5 6 s3 1 POINT POINT 45 2700 3800 7 s 5 8 s3 1 POINT POINT
株主通信：第18期 中間
19 01 02 03 04 290,826 342,459 1,250,678 276,387 601,695 2,128,760 31,096 114,946 193,064 45,455 18,478 10,590 199,810 22,785 2,494 3,400,763 284,979 319,372 1,197,774 422,502 513,081 2,133,357 25,023
1003shinseihin.pdf
1 1 1 2 2 3 4 4 P.14 2 P.5 3 P.620 6 7 8 9 10 11 13 14 18 20 00 P.21 1 1 2 3 4 5 2 6 P7 P14 P13 P11 P14 P13 P11 3 P13 7 8 9 10 Point! Point! 11 12 13 14 Point! Point! 15 16 17 18 19 Point! Point! 20 21
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1 2 3 4 5 6 7 Point 60,000 50,000 40,000 30,000 20,000 10,000 0 29,979 41,972 31,726 45,468 35,837 37,251 24,000 20,000 16,000 12,000 8,000 4,000 0 16,795 22,071 20,378 14 13 12 11 10 0 12.19 12.43 12.40
株主通信 第16 期 報告書
10 15 01 02 1 2 3 03 04 4 05 06 5 153,476 232,822 6,962 19,799 133,362 276,221 344,360 440,112 412,477 846,445 164,935 422,265 1,433,645 26,694 336,206 935,497 352,675 451,321 1,739,493 30,593 48,894 153,612
![[商品カタログ]ゼンリン電子地図帳Ｚｉ16](/thumbs/48/24409875.jpg "[商品カタログ]ゼンリン電子地図帳Ｚｉ16")
-- 0 500 1000 1500 2000 2500 3000 () 0% 20% 40% 60%23 47.5% 16.0% 26.8% 27.6% 10,000 -- 350 322 300 286 250 200 150 100 50 0 20 21 22 23 24 25 26 27 28 29 -- ) 300 280 260 240 163,558 165,000 160,000
ワタベウェディング株式会社
1 2 3 4 140,000 100,000 60,000 20,000 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 5 6 71 2 13 14 7 8 9 10 11 12 1 2 2 point 1 point 2 1 1 3 point 3 4 4 5 6 point 4 point 5 point 6 13 14 15 16 point 17
ヤフー株式会社 株主通信VOL.16
01 260,602264,402 122,795125,595 64,84366,493 107110 120,260123,060 0 500 300 400 200 100 700 600 800 39.8% 23.7% 36.6% 26.6% 21.1% 52.4% 545 700 0 50 200 150 100 250 300 350 312 276 151 171 02 03 04 POINT
WebIntellTN02.qxp (Page 1)
2004 Check Point Software Technologies Ltd. 1 2004 Check Point Software Technologies Ltd. 2 Webサーバ Webアプリケーション データベース Webアプリケーション データベース 2004 Check Point Software Technologies Ltd. 3 2004 Check Point Software
CRA2381-A
AVIC-500/AVIC-5KV /AVIC-505 1 2 63 4 155 11 1 2 3 a a a 3 C O N T E N T S 4 5 6 7 8 1 1 9 10 1 11 12 1 13 14 1 q w e 15 16 2 2 17 18 2 19 20 2 21 22 2 23 24 2 25 26 2 27 28 2 29 30 2 31 32 3 3 33 34 3
/* sansu1.c */ #include <stdio.h> main() { int a, b, c; /* a, b, c */ a = 200; b = 1300; /* a 200 */ /* b 200 */ c = a + b; /* a b c */ }
C 2: A Pedestrian Approach to the C Programming Language 2 2-1 2.1........................... 2-1 2.1.1.............................. 2-1 2.1.2......... 2-4 2.1.3..................................... 2-6
(check matrices and minimum distances) H : a check matrix of C the minimum distance d = (the minimum # of column vectors of H which are linearly depen
Hamming (Hamming codes) c 1 # of the lines in F q c through the origin n = qc 1 q 1 Choose a direction vector h i for each line. No two vectors are colinear. A linearly dependent system of h i s consists
