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(x)10 = xnpn + xn1pn1 +... + x1p1 + x0p0 .
, , , , : 1) , = {0,1}; 2) , = {0, 1, 2, 3, 4, 5, 6, 7}; 3) , = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , , D, , F}, , , , D, , F , , 10, 11, 12, 13, 14, 15.
. 11012 = 1 * 23 + 1 * 22 + 0 * 21 + 1 * 20 = 8 + 4 + 1 = 1310,
1578 = 1 * 82 + 5 * 81 + 7 * 80 = 64 + 40 + 7 = 11110,
A6F16 = 10 * 256 + 6 * 16 + 15 * 1 = 267110.
( ) . ; .
. ={I (1), V (5), (10), L (50), (100), D (500), (1000)}, ( ). ( ): III (3), IV (4), V (5), VI (6), IX (9), XI (11), DCL (650). , , (, IV VI). (, XIV + IV XVIII).
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.
. 110,0012 = 1*22 + 1 * 21 + 0 * 20 + 0 * 2-1 + 0 * 2-2 + 1 * 2-3 = 6,12510;
A,B16 = A * 160 + B * 16-1 = 10 * 1 + 11 * 0,0625 = 10,687510.
- :
, []10, ( ) , ; []p ;
() , {x}10, , , , , {}p; {}p .., ;
() = []p, {}p.
. : 12,810 =?2. :
: 1210 =11002;
: 0,8 *x 2 = 1,6; 0,6 *x 2 = 1,2; 0,2 *x 2 = 0,4; 0,4 *x 2 = 0,8; 0,810 = 0,1100110...2;
: 12,810 = 1100,1100110011...2.
. 29,2510 =?8. 1) 2910 = 358; 2) 0,2510 = 0,28; 3) 29,2510 = 35,28.
. 79,2610 =?16. : 1) 7910 = 4F16; 2) 0,2610 = 0,4016; 3) 79,2610 = 4F,416. , .
2- 8- , 2- 16- , 8- 16- , :
16(0-F) | ||||
A | ||||
B | ||||
C | ||||
D | ||||
E | ||||
F |
8- , 16- . , , ( ) .
. .
2- 8- (- ):
8- 2 (- ):
2- 16- (- ):
16- 2- (- ):
0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 210 = 102 ( ).
0 0 = 0, 1 0 = 1, 1 1 = 0, 0 1 = 10 1 = 1 ( ).
0 * 0 = 0, 0 * 1 = 0, 1 * 0 = 0, 1 * 1 = 1.
0: 0 = , 1: 0 = , 0: 1 = 0, 1: 1 = 1.
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007/002=3,5 ( ).
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×(b-c)=a×b-a×c, = 5, b = 210 =195. 5 × 1 × 5=75. 75 , a×b .
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