2
Outline 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Digital information world 2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.3 2.3.1 2.3.2 2.3.3
2.1 Bit & information amount 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5
2.1.1 Bit binary digit 2 1 1 n 2 n ) 26 5 (16<26<32) http://e-words.jp/w/e38393e38383e38388.html
2.1.2 Bit & Byte http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2102/2102-a.jpg
2.1.2 http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2104/2104-a.jpg
2.1.3 Information amount (Information theory) 1948 A mathematical theory of communication (1) (2) (3) E. Claude Elwood Shannon http://www.cahners-japan.com/news/200102/20010228belllab_shannon.html
entropy H H 2.1.3 = n i= 1 Information amount p i log 2 p i 1/2 1 1 1 1 1 1 H = log2 log2 = ( 1) ( 1) = 1 2 2 2 2 2 2 1/6 A 5/6 B 1 A 5 B 1 1 5 5 1 5 H = log2 log2 = ( 2.58) ( 0.26) = 0.65 6 6 6 6 6 6
2.1.4 (1) http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2106/2106-1-a.jpg
2.1.4 (2) http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2106/2106-1-a.jpg
2.1.4 http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2107/2107-a.jpg
2.1.4 http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2108/2108-a.jpg
2.1.4 http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2109/2109-a.jpg
2.1.4
2.1.4
2.1.5 compression encode decode http://ja.wikipedia.org/wiki/%e3%83%87%e3%83%bc%e3%82%bf%e5%9c%a7%e7%b8%ae
2.1.5 compression http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2110/2110-a.jpg
2.1.5 http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2111/2111-1-a.jpg
2.1.5 http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2111/2111-2-a.jpg
2.1.5 http://kyoiku-gakka.u-sacred-heart.ac.jp/jyouhou-kiki/2112/2112-a.jpg
2.1.5 XVL CAE XVL extensible Virtual world description Language 3D http://www.xvl3d.com/ja/whatsxvl/index.htm http://www.xvl3d.com/ja/demo/engineering.htm
2.1.5 XVL CAE XVL Web3D XVL Web Master
2.1.5 XVL CAE XVL XML D SVG
2.1.5 XVL CAE XVL Web Master
2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5
2.2.1 binary system) 10 decimal system) 16 hexadecimal system)
2.2.2 2 yes or no 10
2.2.3
2.2.4 complement 0011 1100 1101
2.2.5 floating point) a = m 2 e (exponent) (mantissa) (base)
2.3 2.3.1 2.3.2 2.3.3
2.3.1 reliability
2.3.2 parity check) 1 ( ) 0 1 0 0 0 0 0 1 1 ( ) 0 1 0 0 0 0 0 1 0
2.3.2 parity check) 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1
2.3.2 parity check) 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1
2.3.3 Error correction Hamming code) ( ) 1950 Hamming ( ) RAID-2 http://e-words.jp/w/e3838fe3839fe383b3e382b0e382b3e383bce38389e38381e382a7e38383e382af.html
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=0 3 000,001,010,100,101,110,111 2 000 011 110 101 001 010 100 111
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 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1
s1 s2 s3 0 0 0 0 0 1 a 0 1 0 b 0 1 1 c 1 0 0 d 1 0 1 e 1 1 0 f 1 1 1 g 2.3.3 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
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
2.3.3 Hamming code) n1 n2 n3 n4 n5 n6 n7 s1 s2 s3 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1
2.3.3 Hamming code) 16 1010110 S1=0 S2=0 S3=1 s1 = d e f g s2 = b c f g s3 = a c e g 1 0010110 a b c d e f g 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1