- . - . - . - . , .
- , . -. - , . .
:
- :
(-), {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. - :
(), {I, V, X, L, C, D, M}, I =1, V=5, X=10, L=50, C=100, D=500, M=1000.
: - , (, VII=7, XVI=16).
- , , (, IV=4, XL=40).
P AP ={0,1,2,..., P } X, a n a n-1 a n-2...a 1 a 0,a -1 a -2...a -m ( - ; 0; n - , m - ). X X =a nPn +a n-1Pn-1 +...+a 1P1 +a 0P0 +a -1P-1 +a -2P-2 +...+a -mP-m.
.
:
1237,089=1*103+2*102+3*101+7*100+0*10-1+8*10-2+9*10-3
. - (" "-" " .., , , , - ). A2={0,1}.
+ | ||
* | ||
:
101112+11012=1001002; 101112*11012=1001010112; 101112-11012=10102. ( , !)
, 8- 16- . A8={0,1,2,3,4,5,6,7}. A16={0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}( , .. ).
|
|
P Q (Q < P) (Q-P) - P Q. AP AQ, Q - , AP.
:
10- 4 . 72310=0111 0010 00112-10. 8- 3 . 7238=111 010 0112-8.
X, P - a n a n-1 a n-2...a 1 a 0,a -1 a -2...a -m X 10 - .
X =a nPn +a n-1Pn-1 +...+a 1P1 +a 0P0 +a -1P-1 +a -2P-2 +...+a -mP-m, a i 10- .
:
5478 10- . 10- . 5*82+4*81+7*80=359. , 5478 35910.
DF,316 10- . 10- . 13*162+15*161+3*16-1=223,1875. , DF,316 223,187510.