21.

. , , . , , .

, 1 ... . :

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

= / 0, 1 ;

+1 ˠ -I ^

[1, 蠠 =1 .

, +1 .

:

+1

,=1 ; ;

.

, ^=+1 .

. = 2 ( ): 00 000, 01 011, 10 101, 11 110. ( ) 3 + 32 + 32 (,

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

[ (), > ). , . 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% .

.

(248, 233)-, Apple II. , , 256 , . , (check sum), " " (XOR) 256 . , 8 256 . , 256 , , , " " . . . 14 , 9 , pi, p2, ..., p9. CS, ( ) PB (parity bit). pi . p4, p5, p6, 7 , . p2, p3, p8, p9 .

1 2 3 4 5 6 256 CS 1

i

_ _ J _ _

1 1

_ _ L _ _l _ _

L L J

_ _ L

2

_ _ J _ _

_ _ L _ _l _ _

L 1 _i_

 

3

_ _ J _ _

_ _ L _ _l _ _

L 1 L _

;

4

_ _ J _ _

_ _ L _ _l _ _

L 1 1

;

5

_ _ J _ _

_ _ L _ _l _ _

L L J

_ _ L

6

_ _ J _ _

_ _ L _ _l _ _

_!__!__

_ _ 1

7

_ _ J _ _

_ _ L _ _l _ _

L L J

_ _ L

8

_______1_______

L______1_______L______

L______1_____ __J______J_______

______J___

PB

p8'

 

:

 

. 14

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

() , . . = ! ... = 61 ... , ^(,).

= 1 ... . (). , () = =1 *.

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

2.

+ , . . 2 " " (,).

, . . ?(, ) = ( + ).

- , .

, , , , ~(,)(^(,).

, , 1011 0011, 3.

1.

, .

, , , , + 1.

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

, ,

\^2 >~= +1 --1+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.

, ,

, =/+ -߳ . ,

^2 >" = + -1 + + - .

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

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

^ 2, = + , .

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

. (2, 5)- :

1 =00 00000 = 1, 2 = 01 01011 = 2,

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

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

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

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

. , ,

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

-, ( , )-, [20].

, . . , , . , . . , .

► 37

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

► 38

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