24.

(m, )-, , k, , . [l]:

1. (^^-, ,

k, ^k=0 = 2n_m. ;

2. , , k, , , k. ;

3. , k , , k . .

, . : . m, n k (1 < k < n__1), . m, n k .

m, n k , , , , k, k + 1. .

(,)- , . . .

r (m,n)-o, , - (Hamming), m = 2r - r - l n = 2r - l.

, = 1 + 2r - 1 = 2r = 2n_m.

:

1. r. m = 2r - r - l, n = 2r - l;

2. b = b1 b2 ...bn r - (20, 21,... , 2r_1) , . , r = 4, b1 ,b2 ,b4 ,b8 , b3 ,b5 ,b6 ,b7 ,b9, b10, b11, b12, b13, b14, b15 ;

3. M 2r - 1 r . i-

6l . = 2, 3 4 :

0001" 0010 0011 0100 0101

0110 0111

1000 ;

1001 1010 1011 1100

1101 1110

1111

4. = 0, . . , = 3:

+ + + 7 = 0 2 + + + 7 = 0 ; 1 + + + 7 = 0

5. , 3, , , , 3, . 3, = 2*. 4 1- , 2 1 . = 0111 = 0001111.

. + , , . = 0, ( + ) = + = . , , , . - , - . - + , , .

. (4, 7)- = 0001111. 73 3 . , = 0. =

2

01 10 11

7

001 010 011 100 101 110 111

14

0010000. + = 0011111 ( + ) = 011 = , . . . = 0000001, + = 0001110 ( + ) = 111 = 7 . . , . .

, (, )- , -, 2 . 4 , . . 1- 1- , 2- 2-, 4- 4- . . 2 .

. (4, 7)-

3, 5, 7 . 1,2 4 , , \ = 3 + 5 + 67 1101, . . 1,2 4 3, 5 7 .

(, )- . (, + 1)- 4, .

: 2 1:1, 4, 11, 2, 57, ... , .. 8, 1, 32 64 , . (,)-.

(, )-, , . ,

= . ,

1110000

1001100 0101010

1101001

2

^ 2.

+ 1

2 = 2- ^ + 1 = +

+ + 1.

3

- 1 . $1 2 -

, - 2 : $ (1 ^ ^ ) , , - - . $1 , , 3, 5, 7 .., $2 3, 6, 7 . . , = 1 ... = $1 $21 $24$4 5 .. .. £* 2 , $ . $^ ... £* = 0, , . £^ ... £* - . , 1, $ ^ ... £* > , . , , , .

(9,)-, , 100011010.

2 12 4096 9 2 13 4096 _

= < 29 = 512 蠠 ^4 = > 512, .. = 13.

1 2 3 4 5 6 7 8 9 10 11 12 13

$1 $2 1 $3 0 0 0 $4 1 1 0 1 0 . .

1 10 = 00002 210 = 00102 310 = 0011 2 410 = 01002 510 = 0101 2 610 = 01102 710 = 0111 2

810 = 10002

910 = 1001 2 1010 = 10102 11 10 = 1011 2 1210 = 11002 1310 = 1101 2

, 0011000111010. ,

$1 = + 5 + 7 + 9 + + 13 = 0

$2 = + + 7 + + =0

$3 = 5 + + 7 + 12 + 13 = 1 $4 = 9 + + + 12 + 13 = 1

0011100111010. :

#1* = &1 + 63 + 65 + 67 + 69 + 6 + 613 = 1 #* = 62 + 6 + 6 + 67 + 610 + 611 =0 #* = 64 + 65 + 6 + 67 + 612 + 613 = 1 #4* = 6 + 69 + 610 + 611 + 612 + 613 =0

#4 #* #* #* = 01012 = 5.

, .

, .. 2/( + 1) = 2.

8- 4 (212/13 > 28), 16- 5, 32- 6, 64- 7.

► 40

(6,14)-, 5, ?

► 41

(9,)-, , ,

55, 200 1000001000001, 1100010111100, , .