let\'s translate to decimal like this:
1∙102+3∙101+9∙100+8∙10-1+2∙10-2+5∙10-3 = 1∙100+3∙10+9∙1+8∙0.1+2∙0.01+5∙0.001 = 100+30+9+0.8+0.02+0.005 = 139.82510
got It: 139.82510 =139.82510
Translate the number 139.82510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
139 | 2 | | | | | | | |
-138 | 69 | 2 | | | | | | |
1 | -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. | 825*2 |
1 | .65*2 |
1 | .3*2 |
0 | .6*2 |
1 | .2*2 |
0 | .4*2 |
0 | .8*2 |
1 | .6*2 |
1 | .2*2 |
0 | .4*2 |
0 | .8*2 |
the result of the conversion was:
139.82510 = 10001011.11010011002
answer: 139.82510 = 10001011.11010011002