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:
453.6716 = 4 5 3. 6 7 = 4(=0100) 5(=0101) 3(=0011). 6(=0110) 7(=0111) = 10001010011.011001112
answer: 453.6716 = 10001010011.011001112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
4∙162+5∙161+3∙160+6∙16-1+7∙16-2 = 4∙256+5∙16+3∙1+6∙0.0625+7∙0.00390625 = 1024+80+3+0.375+0.02734375 = 1107.4023437510
got It: 453.6716 =1107.4023437510
Translate the number 1107.4023437510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1107 | 2 | | | | | | | | | | |
-1106 | 553 | 2 | | | | | | | | | |
1 | -552 | 276 | 2 | | | | | | | | |
| 1 | -276 | 138 | 2 | | | | | | | |
| | 0 | -138 | 69 | 2 | | | | | | |
| | | 0 | -68 | 34 | 2 | | | | | |
| | | | 1 | -34 | 17 | 2 | | | | |
| | | | | 0 | -16 | 8 | 2 | | | |
| | | | | | 1 | -8 | 4 | 2 | | |
| | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 40234375*2 |
0 | .80469*2 |
1 | .60938*2 |
1 | .21875*2 |
0 | .4375*2 |
0 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1107.4023437510 = 10001010011.011001112
answer: 453.6716 = 10001010011.011001112