. . , , , , .
, , , , . , 10 - - "0123456789".
, , . , , - . , , , . , , .
, , 246. , , . , :
246 = 200 + 40 + 6 = 2 * 102 + 4 * 101 + 6 * 100
. : 2 * 102 + 4 * 101 + 6 * 100 . :
. "2" 3. 10 . "4" 2 10 . , . , . , N . i- ai. : anan-1.a2a1. , :
anan-1.a2a1 = an * 10n-1 + an-1 * 10n-2 + . + a2 * 101 + a1 * 100
ai "0123456789"
. . , , " ", "". , . . , :
anan-1.a2a1 = an * 5n-1 + an-1 * 5n-2 + . + a2 * 51 + a1 * 50
ai "012345"
, 10 . , 10 2. :
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|
anan-1.a2a1 = an * 2n-1 + an-1 * 2n-2 + . + a2 * 21 + a1 * 20
ai "01"
- , 0 1.
: 10, 111, 101.
. , .
. . , , 1011. . :
1001 = 1 * 23 + 0 * 22 + 0 * 21 + 1 * 20
:
1 * 23 + 0 * 22 + 0 * 21 + 1 * 20 = 8 + 0+ 0 + 1 = 9.
, , 1011() = 9 (). . , , , . ( ). . .
. : ) 10010 ) 11101 ) 1010 ) 1110 ) 100011 ) 1100111 ) 1001110
( , ).
, . , 9, , . ( , , .)
.
, ( ).
- 0 1 - ,
- 2, - 0, 1,
- 3 ( , ), - 1 ).
: 10011 + 10001.
: 1+1 = 2. 0 1 .
: 1+0+1 ( ) =2. 0 1 .
: 0+0+1( ) = 1. 1.
: 0+0=0. 0.
: 1+1=2. 0 1.
.
10011 = 1*24 + 0*23 + 0*22 + 1*21 + 1*20 = 16 + 2 + 1 =19
10001 = 1*24 + 0*23 + 0*22 + 0*21 + 1*20 = 16 + 1 = 17
100100 = 1*25 + 0*24 + 0*23 + 1*22 + 0*21 + 0*20 =32+4=36
17 + 19 = 36 -
:
) 11001 +101 =
) 11001 +11001 =
) 1001 + 111 =
) 10011 + 101 =
|
|
) 11011 + 1111 =
) 11111 + 10011 =
. - . , .
, . , . 12.
. 22 = 4, . 23 = 8, 24=16 . 23 =8. 12 - 8 = 4. 4.
. 4 = 22.
12 = 23 + 22. 4, = 3, , 1 0. , , : 1*23 + 1*22 +0*21 + 0*20 = 1100 - 12. , - , .
. 23.
1. 24 = 16. 23 -16= 7.
2. 22 = 4. 7 - 4 = 3
3. 21 = 2. 3 - 2 = 1
4. 20=1 1 - 1 =0
: 1*24 + 0*23 +1*22 +1*21 +1*20
10111
, , . :
= 2
= 2
, . 19.
= 19
1
= 1
= 9
2
= 1
= 4
3
= 0
= 2
4
= 0
= 1
5
= 1
= 0
10011. , . - , .
) 14 ) 29 ) 134 ) 158 ) 1190 ) 2019
.
, . , / . < >.
, , - , . ( , 20/6), , .
. , , N . , M - ,
2m > 10N
, 5,401
:
, 101. 2.
1: 2-2 = 0,25; 0,401 - 0,25 = 0,151. - .
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2: 0,151. : 2-3 = 0,125; 0,151 - 0,125 = 0,026
, , 2-2 +2-3 . : 0,011. , , 2-1 .
, . . , 103 2. 1000<2M. , 29 = 512 210 = 1024. .
3: 0,026. 2-6 = 0,015625; 0,026 - 0,015625 = 0,010375 : 0,011001. , , .
4: 0,010375. 27 = 0,0078125;
0,010375 - 0,0078125 = 0,0025625
5: 0,0025625. 2-9 = 0,001953125;
0,0025625 - 0,001953125 = 0,000609375
2-10 , 2-11, , , , .
0,401 = 0,011001101
, , . .
:
: . N .
1. 10N < 2M
2: ( ). .
1. = 1
2. 2- >
1
= - 2-
3. = + 1
4. >
2.
) 3,6 ) 12,0112 ) 0,231 ) 0,121 ) 23, 0091
, , . , , , . :
- | ||||
= |
. 1 - 0 =1. 1.
0 -1. . . , ( ) 2-1 =1. 1.
. , 0 . 2-1 =1. 1.
1101 - 110 = 13 - 6 = 7 (111) .
, . , , . , 10010 011011.
|
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, .
: 34 - 22 = 12
. 100010 - 10110 = 1100
10110 :
01001 + 00001 = 01010.
:
100010 + 01010 = 101100.
. , 001100. 1100,