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{ x1, x2, , xn },
2) () .
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:
0, 1, 2, 3, 4, , 9;
: 0, 1;
:
1, 5, 10, 50, 100, 500, 1000, , , : I, V, X, L, C, D, M;
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0, 1 0, 1, 2, 3, 4, 5, 6, 7 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , , D, E, F |
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. j - xi, j - , , :
, , .
, ( 1): K K . K , 0. , K - {0, 1, 2,..., K-1 }.
- :
() = xn-1Kn-1 + xn-2Kn-2 + + x1K + x0K0 + x-1K-1 + x-2K-2 + + x-mK-m =
= (1)
xi i ;
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n, m , ;
i .
( ) .
:
23,43 (10) = 2×101 + 3×100 + 4×10-1 + 3×10-2
( 3 , - );
451,2 (8) = 4×82 + 5×81 + 1×80 + 2×8-1.
, . , , , :
() = xn-1 xn-2 x1 x0, x-1 x-2 x-m.
, : , , 0, 1, 2,..., - 1, , , - 1, - 2,...., - . , .
1 , . , , .
n - 1 | n - 2 | -1 | -2 | -m |
1 -