21.

. , , . , , .

, ! ... . :

(1 . . . ) = ! . . . +! ,

= / 0, ^ ! ; [ 1, 蠠 =! .

, ^+! .

D(a1 ...am am+1) / \

:

Em+1 i=1 ai ;

{), .

, X^ZLi1 .

. m = 2 ( E): 00 , 01 011, 10 101, 11 110. ( ) q3 + 3pq2 + 3p2q (, ). , . 3pq2. 2pq + q2. q , 3pq2 < 2pq + q2.

(m, )- . , , . m E. D . 3m. i (1 ^ i ^ m) i, i+m, i+2m : , . , p3. 3p2q. p3 +3p2q. , q3 + 3pq2.

. q = . . .28, . . % 2.8%.

q5 + 5pq4 + 10p2 q3 = 0.00856 = 0.856%,

. . %. 10 0.910 ~ 35% 0.97210 ~ 75% 0.9914410 ~ 92% .

.

(2048, 21)-, Apple II. , , 256 , . , (check sum), " " (XOR) 256 . , 8 256 . , 256 , , , " " . . . 5 , 9 , pL, p2, ..., p9. CS, ( ) PB (parity bit). p1 . P4, P5, P6, P7 , . P2, P3, Pe, P9 .

1 2 3 4 5 25 CS 1

1

1

_ _ J _ _

1 'Pi

_ _ L _ J _ _

1 1

L L _

 

_ _ L

2

_ _ J _ _

1 1 _ _ L _ J _ _

1 'P3

_ _ L _ _ l_ _

 

 

3

1

. _ J _ _

_ _ L _ J _ _

1 1 _ _ L _ _ 1 _ _

 

_ _ 1 _

4

1

1 1 _ _ |_ _ _l _ _

1 1 _ _ |_ _ _ l_ _

 

1

_ _ l_

5

1

_ _ J _ _

■P5 1

_ _ L _ J _ _

1 1

L L _

 

_ _ L

1

. _ J _ _

1 1 _ _ L _ J _ _

1 1 _ _ L . _ 1 _ _

 

_ _ 1

7

1

. _ J _ _

_ _ L _ J _ _

1 1 _ _ L _ _ l_ _ _

 

_ _ L

8

1

,......L......

1 1

L......L......L......

1 1

L......L......J......j

 

1

......J___

PB

1 1

1 'P9

 

 

. 15

. , . , (, )- . , . .

() , . . = ! ... = ! ... , /(,).

= \ ... . (). , () = ^ =1 .

. = 1001 = 0011, () = () = 2, <(, ) =

2.

+ , . . 2 " " ().

, . . <(, ) = ( + ).

- , .

, , , , -(,)(^(,).

, , 1011 0011, 3.

1.

, .

, , , , + 1.

: , , , . : ' < + 1, ' .

, ,

^2 >~( = +1 --1 + + ^1 -1 +

=+1

~ [ ] ~ --1 +1.

, , , 2 + 1.

, ,

: , , . . 2. , , , , , . , 2.

. (1,3)-, , 0 000 1 111, , 000 0,001 0,010 0,011 1,100 0,101 1,110 1,111 1. ( ) , . . 3.

,

. = 1 ... = 1 ... . = 1 ... , = 1... , ҳ = { + (1 ^ ^ ). , , ( ) . , , , , , .

. = 01 = 0110, = 0010. = 0100. , , 0110 01.

^ 2, = + , .

. (2, 3)- . {000,011,101,110}. 001, 010, 100, 111 . .

 

 

,- = + 1-1 + + - .

=0

. (2, 5)- : 1 =00 00000 = 1, 2 = 01 01011 = 2,

= 10 10101 = , 4 = 11 11110 = 4.

, . , ^(ܳ,j) ^ 3 = , , , 1 , . , , , . 5 + 54.

[20], ( , )-, 2 + 1, , ( )

> ^2 ( + -1 + + + 1),

. , ,

> lg2 (--1 + --2 + + -1 + 1),

--, ( , )-, [20].

, . . , , . , . . , .

► 36

(8, 9)- . , , 1%. . , .

► 37

, , 1. = 32, 1 = 3 = 23, 1 = 7.