GNU Free Documentation License . .

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(10)
2, 3, 4, 5, 6, 7, 8, 9, 12, 16, 60
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  2. , (0 1).

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  • 8 64 , 3- 6- , . , ( 0 63), XI . , , , .
  • , , ( ) .
  • XVII Explication de lArithmétique Binaire[8]. 0 1, . , , , 0 111111. , .[9]

[]

(a b) 2. ( ) :

\ x_{2,2} = (a_{n-1} a_{n-2}\dots a_{1} a_{0})_{2,2} = \sum_{k=0}^{n-1} a_k b^k,

:

  • \ x_{2,2} ,
  • \ (.\ .\ .)_{2,2} , ,
  • \ n  () x2,2,
  • \ k  ,
  • \ a_k x2,2 a={0,1}, 2,
  • \ b=2  , ,
  • \ b^k=2^k , .

:

\ x_{2,2} = (za_{n-1} a_{n-2}\dots a_{1} a_{0})_{2,2} = z\sum_{k=0}^{n-1} a_k b^k,

:

  • \ z z={+,-}, .

:

F(X) = \sum\limits_{n=0}^{\infty}a_nX^n,

an R=a{0,1}, X=2, n=k, \infty   n-1.

  b x2,b .
- b .
- a, :

\bar{A}(a,n)=\bar{A}_a^n=a^n=2^n,

a=2  2- a={0,1} ak, n  () x2,b.

:

x_{2,2} = (a_{n-1} a_{n-2}\dots a_{1} a_{0},a_{-1} a_{-2}\dots a_{-(m-1)} a_{-m})_{2,2} = \sum_{k=-m}^{n-1} a_k b^k,

:

  • \ m  ,
  • \ a_k  \ a_k={0,1}, 2,
  • \ b=2  , .

, , , . : - , ,   .

[] ,

+ 0 1
0 0 1
1 1 10

«» (14 + 5 = 19):

1
+ 1 1 1 0
1 0 1
1 0 0 1 1


- 0 1
0 0 1
1 1 0


× 0 1
0 0 0
1 0 1

«» (14 × 5 = 70):

× 1 1 1 0
1 0 1
+ 1 1 1 0
1 1 1 0
1 0 0 0 1 1 0

[]

2:

512 256 128 64 32 16 8 4 2 1

1 . , 1, .

[]

, 110001. :

1\times 2^0 + 0\times 2^1 + 0\times 2^2 + 0\times 2^3 + 1\times 2^4 + 1\times 2^5 = 1\times 1 + 0\times 2 + 0\times 4 + 0\times 8 + 1\times 16 + 1\times 32= 49.

:

512 256 128 64 32 16 8 4 2 1
1 1 0 0 0 1
+32 +16 +1

, , . . .
, 110001 49.

[]

:

, , , ( 2). , 1011011 : 0*2+1=1 >> 1*2+0=2 >> 2*2+1=5 >> 5*2+1=11 >> 11*2+0=22 >> 22*2+1=45 >> 45*2+1=91 91. 101111 : 0*2+1=1 >> 1*2+0=2 >> 2*2+1=5 >> 5*2+1=11 >> 11*2+1=23 >> 23*2+1=47 47. 1) 0,11012=0,X10 ( )
1:2=0,5
0,5+0=0,5
0,5:2=0,25
0,25+1=1,25
1,25:2=0,625
0,625+1=1,625
1,625:2=0,8125
: 0,11012= 0,812510
2) 0,3568=0,X10 ( )
6:8=0,75
0,75+5=5,75
5,75:8=0,71875
0,71875+3=3,71875
3,71875:8=0,46484375
: 0,3568=0,4648437510
3) 0,A6E16=0,X10 ( )
14:16=0,875
0,875+6=6,875
6,875:16=0,4296875
0,4296875+10=10,4296875
10,4296875:16=0,65185546875
: 0,A6E16=0,6518554687510

[]

, 19 .  :

19 /2 = 9    1
9  /2 = 4  c  1
4  /2 = 2    0
2  /2 = 1    0
1  /2 = 0    1

, 2 . , 0. . .. ... 19 : 10011.

[]

1011010.101 . :

\begin{align}&1\times 2^6 + 0\times 2^5 + 1\times 2^4 + 1\times 2^3 + 0\times 2^2 + 1\times 2^1 + 0\times 2^0 + 1\times 2^{-1} + 0\times 2^{-2} + 1\times 2^{-3} = \\ &= 1\times 64 + 0\times 32 + 1\times 16 + 1\times 8 + 0\times 4 + 1\times 2 + 0\times 1 + 1\times \frac{1}{2} + 0\times \frac{1}{4} + 1\times \frac{1}{8} = 90,625 \end{align}

[]

:

  • ;
  • ;
  • , ;
  • , . .

: 206,116 .

20610=110011102 ; 2, :

.116 2 = 0.232
.232 2 = 0.464
.464 2 = 0.928
.928 2 = 1.856
.856 2 = 1.712
.712 2 = 1.424
.424 2 = 0.848
.848 2 = 1.696
.696 2 = 1.392
.392 2 = 0.784
 . .
: 206,11610=11001110,00011101102

[]

[]

, :

  • , , . , :  ( )  ( ), ( )  . .
  • , . , , , , .[   555 ]
  • .   .

() , (0,1).

[]

, , : 5¾, 715/16, 311/32 . .

[] .

[] -

1 2
2 4
3 8
4 16
5 32
6 64
7 128
8 256
9 512
10 1024
11 2048
12 4096
13 8192
14 16384
15 32768
16 65536
17 131072
18 262144
19 524288
20 1048576
21 2097152
22 4194304
23 8388608
24 16777216
25 33554432
26 67108864
27 134217728
28 268435456
29 536870912
30 1073741824
31 2147483648
32 4294967296
33 8589934592
34 17179869184
35 34359738368
36 68719476736
37 137438953472
38 274877906944
39 549755813888
40 1099511627776
41 2199023255552
42 4398046511104
43 8796093022208
44 17592186044416
45 35184372088832
46 70368744177664
47 140737488355328
48 281474976710656
49 562949953421312
50 1125899906842624

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  1. Sanchez, Julio & Canton, Maria P. (2007), Microcontroller programming: the microchip PIC, Boca Raton, Florida: CRC Press, p. 37, ISBN 0-8493-7189-9 
  2. W. S. Anglin and J. Lambek, The Heritage of Thales, Springer, 1995, ISBN 0-387-94544-X
  3. Ordish George, Hyams, Edward. The last of the Incas: the rise and fall of an American empire.  New York: Barnes & Noble, 1996.  . 80.  ISBN 0-88029-595-3
  4. Experts 'decipher' Inca strings. 18 2011.
  5. Carlos Radicati di Primeglio, Gary Urton Estudios sobre los quipus.  P. 49.
  6. Dale Buckmaster (1974). «The Incan Quipu and the Jacobsen Hypothesis». Journal of Accounting Research 12 (1): 178-181. 2009-12-24.
  7. Bacon, Francis, The Advancement of Learning, vol. 6, London, pp. Chapter 1, <http://home.hiwaay.net/~paul/bacon/advancement/book6ch1.html> 
  8. http://www.leibniz-translations.com/binary.htm Leibniz Translation.com EXPLANATION OF BINARY ARITHMETIC
  9. Aiton, Eric J. (1985), Leibniz: A Biography, Taylor & Francis, pp. 2458, ISBN 0-85274-470-6 

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