.
1928 . . . :
I = log2 K,
- ;
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K=2I.
:
I = log2 K = log2 (1 / ) = - log2 ,
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= 1/, =1/.
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I = log2 3 = 1,585 .
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I = - Sum i log2 i,
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I = -(1/2 log21/2 + 1/4 log21/4 + 1/8 log21/8 + 1/8 log21/8) = 1/2 + 2/4 + 3/8 + 3/8 = 14/8 = 1,75 ().
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( - 8) | ||||
11110010 11101001 11101101 | ||||
11101101 11101001 11110010 | ||||
! | 11101101 11101001 11110010 11110101 00100000 11101101 1110101 11110010 00100001 | |||
(** */ | 00101000 00101010 00101010 00100000 00101010 00101111 |
: (. bi nary digi t - ) (byte).
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, 210 = 1024 .
, 1 = 210 = 1024 = 220 = 1 048 576 .
1 = 210 = 220 = 230 = 1 073 741 824 .
100 :
50 000 150 | |
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CD - | 10 |
15 | |
1000 |
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1928 .. :
I = log2 N 2I = N,
N ( ),
I - .
N = 2 ( ), I = 1 .
, , k 2k 2 , . 2k , I .
. N p = 1 / N, N = 1 / p :
I = log2 (1/p) = - log2 p
N, . . 1948 .
, . 90 , ~ 40 , ~ 2 , ~ 200 . 200 1000, 0.2, , . (pa) 0.2. , p = 0.04, p = 0.002, = 0.09.
.. 0.2 , , - . . ,
hi = log2 1/pi = - log2 pi,
pi - i- .
hi, ,
H = Sum pi hi = - Sum pi log2 pi
, pi
pi = 1 / N.
.
( ) , .
- {0, 1}.
- .
- .
- , .
1 | ||
1 | = 8 | |
1 () | = 210 = 1024 | ~ 1 |
1 () | = 210 = 220 | ~ 1 |
1 () | = 210 = 230 | ~ 1 |
( ) - , , (, ..).
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( , 1) 0. , . .
, :
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|
1). .
I = log2 N 2I = N,
N - ( ),
I - .
2). .
I = log2 (1/p) = - log2 p
p - N .
3). .
H = S pi hi = - S pi log2 pi
pi - i- ;
hi = log2 1/pi = - log2 pi - , ;
-
.