(c/c) . (.. , ) . , II ( ) .
() , . , 757,7 7 , 7 , 7 . 757,7 700 + 50 + 7 + 0,7 = 7 ∙ 102 + 5 ∙ 101 + 7 ∙100 + 7 ∙ 101 = 757,7.
c/c , . . , : , , .. q an 1∙ qn 1 + an 2∙ qn 2 +... + a 1∙ q 1 + a 0∙ q 0 + a 1∙ q 1 +... + a m ∙ q m , n m , .
/ (), /. , / 10, (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) /. / 0 1, 16, 10, 11, 12, 13, 14, 15 / () A, B, C, D, E, F, , .. .
10 ( 10 ). , , . , /, 2. / , .
/ , 2, , .
(. 1.1).
1.1
/
/c | /c | /c | /c |
B | |||
C | |||
D | |||
E | |||
F | |||
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, 2 / , . /c () () , ( 8 16 , 2).
8- 16- 2- /c
( ) ( ).
502(8 c/c) →? (2 c/c)
502(8 c/c) = 101000010 (2 c/c)
2- /c 8- 16-
( ) . .
1111110(2 c/c) →? (8 c/c)
1111110 (2 c/c) = 001111110 (2 c/c) = 176(8 c/c)
1111010101,1100(2 c/c) →? (16 c/c)
001111010101, 1100 (2 c/c) = 3D5,C(16 c/c).
/ 10-
/ k a 1 ...an /, a 1,..., an . : a 1 ∙ kn 1 +a 2 ∙ kn 2 +...+an ∙ k 0.
110011(2 c/c) →? (10c/c)
110011(2 c/c) = 1 ∙ 10101+1 ∙ 10100+0 ∙ 1011+0 ∙ 1010+1 ∙ 101+1 ∙ 100(2 c/c)=
=1∙ 25+1∙ 24+0∙ 23+0∙ 22+1∙ 21+1∙ 20 (10 c/c)= 32 + 16 + 2 + 1 = 51(10 c/c),
1216,04(8 c/c) →? (10 c/c)
1216,04(8 c/c) = 1 ∙ 83 + 2 ∙ 82 + 1 ∙ 81 + 6 ∙ 80+4 ∙ 82= 512 + 128 + 8 + 6 + 0,0625 = 654,0625(10 c/c).
10 /c
, . /, . : r ( /c), ( 0 r 1) . : r, r, . , r. : / r. ( ), /c.
, 25(10 c/c) 2- /c. , 11001(2 c/c). :
25(10 c/c) = 11001(2 c/c) = 1 ∙ 24 + 1 ∙ 23 + 0 ∙ 22 + 0 ∙ 21 + 1 ∙ 20 = 25(10 c/c).
/c r c/c q ( , ) /c q , : ; ( ). /c , . , /c.
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0,3125(10 c/c) →? (8 c/c)
0,3125(10 c/c) = 0,24(8 c/c)
/ , , , .