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:
5a9.b416 = 5 a 9. b 4 = 5(=0101) a(=1010) 9(=1001). b(=1011) 4(=0100) = 10110101001.1011012
answer: 5a9.b416 = 10110101001.1011012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
5∙162+10∙161+9∙160+11∙16-1+4∙16-2 = 5∙256+10∙16+9∙1+11∙0.0625+4∙0.00390625 = 1280+160+9+0.6875+0.015625 = 1449.70312510
got It: 5a9.b416 =1449.70312510
Translate the number 1449.70312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1449 | 2 | | | | | | | | | | |
-1448 | 724 | 2 | | | | | | | | | |
1 | -724 | 362 | 2 | | | | | | | | |
| 0 | -362 | 181 | 2 | | | | | | | |
| | 0 | -180 | 90 | 2 | | | | | | |
| | | 1 | -90 | 45 | 2 | | | | | |
| | | | 0 | -44 | 22 | 2 | | | | |
| | | | | 1 | -22 | 11 | 2 | | | |
| | | | | | 0 | -10 | 5 | 2 | | |
| | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 703125*2 |
1 | .40625*2 |
0 | .8125*2 |
1 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1449.70312510 = 10110101001.1011012
answer: 5a9.b416 = 10110101001.1011012