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:
7AB.43216 = 7 A B. 4 3 2 = 7(=0111) A(=1010) B(=1011). 4(=0100) 3(=0011) 2(=0010) = 11110101011.010000110012
answer: 7AB.43216 = 11110101011.010000110012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
7∙162+10∙161+11∙160+4∙16-1+3∙16-2+2∙16-3 = 7∙256+10∙16+11∙1+4∙0.0625+3∙0.00390625+2∙0.000244140625 = 1792+160+11+0.25+0.01171875+0.00048828125 = 1963.2622070312510
got It: 7AB.43216 =1963.2622070312510
Translate the number 1963.2622070312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1963 | 2 | | | | | | | | | | |
-1962 | 981 | 2 | | | | | | | | | |
1 | -980 | 490 | 2 | | | | | | | | |
| 1 | -490 | 245 | 2 | | | | | | | |
| | 0 | -244 | 122 | 2 | | | | | | |
| | | 1 | -122 | 61 | 2 | | | | | |
| | | | 0 | -60 | 30 | 2 | | | | |
| | | | | 1 | -30 | 15 | 2 | | | |
| | | | | | 0 | -14 | 7 | 2 | | |
| | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | 1 | | |
 |
the Fractional part of the number is multiplied by the base of the new number system:
 |
0. | 26220703125*2 |
0 | .52441*2 |
1 | .04883*2 |
0 | .09766*2 |
0 | .19531*2 |
0 | .39063*2 |
0 | .78125*2 |
1 | .5625*2 |
1 | .125*2 |
0 | .25*2 |
0 | .5*2 |
the result of the conversion was:
1963.2622070312510 = 11110101011.01000011002
answer: 7AB.43216 = 11110101011.01000011002