101,012=1*22+0*21+1*20+0*2-1+1*2-2=4+0+1+0+1/4=5,2510
253,318=2*82+5*81+3*80+3*8-1+1*8-2 =128+40+3+3/8+1/64=171+0,375+0,015625=171,39062510
42D16=4*162+2*161+13*160=1024+32+13=106910
. , .
, .
34 / 2 = 17 (0)17 / 2 = 8 (1)8 / 2 = 4 (0)4 / 2 = 2 (0)2 / 2 = 1 (0)1 / 2 = 0 (1)
3410 = 1000102
472 / 8 = 59 (0)59 / 8 = 7 (3)7 / 8 = 0 (7)
47210 = 7308
924 / 16 = 57 (12)57 / 16 = 3 (9)3 / 16 = 0 (3)
92410 = 39C16
. . . .
0,225 * 2 = 0,450,45 * 2 = 0,90,9 * 2 = 1,80,8 * 2 = 1,60,6 * 2 = 1,20,2 * 2 = 0,4
0,22510 = 0,001110012
0,225 * 8 = 1,80,8 * 8 = 6,40,4 * 8 = 3,20,2 * 8 = 1,60,6 * 8 = 4,8
0,22510 = 0,163148
0,225 * 16 = 3,60,6 * 16 = 9,60,6 * 16 = 9,6
0,22510 = 0,69916
, , .. ( , .).
:
0 + 0 = 01 + 0 = 10 + 1 = 11 + 1 = 10, , , . , ( 2) ( ).
:
1101+ 101 ------ 10010
:
0 - 0 = 01 - 0 = 10 - 1 = ( ) 11 - 1 = 0:
1110- 101 ---- 1001
:
0 * 0 = 01 * 0 = 00 * 1 = 01 * 1 = 1:
1110* 10------+ 0000 1110 ------ 11100
:
1110 | 10 |----10 | 111---- 11 10---- 10 10---- 0
, : . , :
|
|
XXXV = 10+10+10+5 = 35; CCXIX = 100+100+101+10 = 219;
:
( : 2, 1000, 4, 100, 2, 10, 5)
2, 2000 20.
2´ 1000 + 4´ 100+2´ 10+5 = 2425
() - ( 4-5 ), . , , , , (IV = (51) = 4; VI = (5+1) = 6).
, . , . , , . , , 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 10, 10, . 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ( 10, 100, 1000, 10000 . . ). 10, . , .
. 10? , , 10 . . , . . . . , 12, . , , . , ? , . .
, .
, , , .
- , 80 - .
, - , V , , X .
() () . 10- . 10- 0 9, , 450 (1- 0, 2- 5, 3- 4), 4F5 , F 0 9.
() () . . 60 ( 00 59), 24 ( 00 23), 365 . .
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(), . , 100 , 100 .
. , , , , . , 3, 5, 10 . , . , 5 10 (). .
() 1, 10, 102, 103, 104, 105, 106, 107. :
? . 10, 1. , 10 , 10 - .
, , . . , . 345:
, 2 : . . . 32:
60 , 1. .
1 59 , 60. 92:
, . 92 92=60+32, , , 3632=3600+32. , 0 :
3632 , :
, . , , 60 , 60 .
. 1, 5, 10, 50, 100, 500 1000 I, V, X, L, C, D M . . :
1. . , 32 XXXII=(X+X+X)+(I+I)=30+2=32
2. , . , : , L(50) (100) X(10), D(500) M(1000) C(100), V(5) I(1); 444 CDXLIV = (D-C)+(L-X)+(V-I) = 400+40+4=444.
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3. , 1 2 .
, () , :
1)
2) ()