This transfer is possible in two ways: direct transfer and using the decimal system.
first, let\'s make a direct transfer.
let\'s do a direct translation from hexadecimal to binary like this:
18e.7816 = 1 8 e. 7 8 = 1(=0001) 8(=1000) e(=1110). 7(=0111) 8(=1000) = 110001110.011112
answer: 18e.7816 = 110001110.011112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙162+8∙161+14∙160+7∙16-1+8∙16-2 = 1∙256+8∙16+14∙1+7∙0.0625+8∙0.00390625 = 256+128+14+0.4375+0.03125 = 398.4687510
got It: 18e.7816 =398.4687510
Translate the number 398.4687510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
398 | 2 | | | | | | | | |
-398 | 199 | 2 | | | | | | | |
0 | -198 | 99 | 2 | | | | | | |
| 1 | -98 | 49 | 2 | | | | | |
| | 1 | -48 | 24 | 2 | | | | |
| | | 1 | -24 | 12 | 2 | | | |
| | | | 0 | -12 | 6 | 2 | | |
| | | | | 0 | -6 | 3 | 2 | |
| | | | | | 0 | -2 | 1 | |
| | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 46875*2 |
0 | .9375*2 |
1 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
398.4687510 = 110001110.011112
answer: 18e.7816 = 110001110.011112