5
1.
2.
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2.4.
3.
4.
1.
.
2.
- , , .
. . , , , ( ), .
O (), . , .
.
, q.
, , ( - , - ..).
, , .
:
(q) ‑ q;
‑ ;
n + m ‑ .
, :
. , n. :
:
.
. (0-9). , .
10 , : , , ..
, 372,45 :
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372,45=3*102+7*101+2*100+4*10-1+5*10-2
- . , , : 0 1.
2, 10 (: -), 11 (-), - 100 (--) ..
. :
1010111,11=1*26+0*25+0*24+0*23+1*22+1*21+1*20+1*2-1+1*2-2
. :
, , , (0 1), , 2 ( , , );
( ) .
, , , 3,3 .
. 8 : 0,1,2,3,4,5,6,7. - 10 "" (q =8).
0 7 .
, 247 167:
247(8) = 2*82+4*81+7*80 = 128+32+7 = 167(10)
( ), , . , . 16 10 (0-9) 6 (A, B, C, D, E, F) 10, 11, 12, 13, 14, 15.
q = 16(10) = 10(16). :
DAC5E(16) = 13*164+10*163+12*162+5*161+14*160 = 855054(10).
, , .
: 746(8), 1011(2), 365(10), 7D(16).
(q =10) (q =2), ( 0 16) ( 1).
N, R, Q Q R , Q. Q , Q, .., , Q. N Q , ( , N ).
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1
q=10 | q=2 | q=8 | q=16 |
A | |||
B | |||
C | |||
D | |||
E | |||
F | |||
:
(10) = 22 (10) = 8625 .
22(10) =10110(2)
48 | |||
8625(10) =211(16)
, R, Q Q R, . N Q . ( , ). .
. 0,7243.
R=10. Q=2.
0,7243 ( 2) ( /). , , :
:
0,7243 * 2 = 1,4486 1 ->
0,4486 * 2 = 0,8972 0
0,8942 * 2 = 1,7944 1
0,7944 * 2 = 1,5888 1
0,5888 * 2 = 1,1776 1
0,1776 * 2 = 0,3552 0
0,3552 * 2 = 0,7104 0
0,7243 -> 0,101110.
, . , .
, . , .
. , .. , - , .
: (10) = 22,125 (10) .
(10) = 22 (10) = 10110 (2); (10) = 0,125 (10) =0,001(2);
(10) = 22,125 (10) =10110,001(2).
. (16=24). - . 2.
2
Q=10 | ||||||||
Q=16 | ||||||||
Q=10 | ||||||||
Q=16 | A | B | C | D | E | F | ||
:
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5C3F(16) = 101 1100 0011 1111(2)
97,D3(16) = 1001 1010 0111, 1101 0011(2)
.. ( ) . - , ‑ . ( , . 1), , - , . , . .
:
1 0101 1101 0111, 1011 011(2) q 16
0001 0101 1101 0111, 1011 0110(2) = 15D7,B6(16)
, , .
, , (, , . 1), , .
:
1447(10) = 5A7(16)
57(16) = 0101 1010 0111(2) = 010 110 100 111(2)
57(16) = 2 6 4 7 (8)
8,8(10) =1000,1100 1100 1100(2) = 001 000,110 011 001 100(2)
8,8(10) = = 1 0, 6 3 1 4 (8)
. , .. .
:
(2) =11101,11(2) = 1*24+1*23+1*22+0*21+1*20+1*2-1+1*2-2 =
= 16+8+4+1+1/2+1/4 = 29,75(10)
(16) =2,8(16) =10*162+2*16+12+8/16 =2560+32+12+0,5 = 2544,5(10).
.