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:
123ABC.5616 = 1 2 3 A B C. 5 6 = 1(=0001) 2(=0010) 3(=0011) A(=1010) B(=1011) C(=1100). 5(=0101) 6(=0110) = 100100011101010111100.01010112
answer: 123ABC.5616 = 100100011101010111100.01010112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙165+2∙164+3∙163+10∙162+11∙161+12∙160+5∙16-1+6∙16-2 = 1∙1048576+2∙65536+3∙4096+10∙256+11∙16+12∙1+5∙0.0625+6∙0.00390625 = 1048576+131072+12288+2560+176+12+0.3125+0.0234375 = 1194684.335937510
got It: 123ABC.5616 =1194684.335937510
Translate the number 1194684.335937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1194684 | 2 | | | | | | | | | | | | | | | | | | | | |
-1194684 | 597342 | 2 | | | | | | | | | | | | | | | | | | | |
0 | -597342 | 298671 | 2 | | | | | | | | | | | | | | | | | | |
| 0 | -298670 | 149335 | 2 | | | | | | | | | | | | | | | | | |
| | 1 | -149334 | 74667 | 2 | | | | | | | | | | | | | | | | |
| | | 1 | -74666 | 37333 | 2 | | | | | | | | | | | | | | | |
| | | | 1 | -37332 | 18666 | 2 | | | | | | | | | | | | | | |
| | | | | 1 | -18666 | 9333 | 2 | | | | | | | | | | | | | |
| | | | | | 0 | -9332 | 4666 | 2 | | | | | | | | | | | | |
| | | | | | | 1 | -4666 | 2333 | 2 | | | | | | | | | | | |
| | | | | | | | 0 | -2332 | 1166 | 2 | | | | | | | | | | |
| | | | | | | | | 1 | -1166 | 583 | 2 | | | | | | | | | |
| | | | | | | | | | 0 | -582 | 291 | 2 | | | | | | | | |
| | | | | | | | | | | 1 | -290 | 145 | 2 | | | | | | | |
| | | | | | | | | | | | 1 | -144 | 72 | 2 | | | | | | |
| | | | | | | | | | | | | 1 | -72 | 36 | 2 | | | | | |
| | | | | | | | | | | | | | 0 | -36 | 18 | 2 | | | | |
| | | | | | | | | | | | | | | 0 | -18 | 9 | 2 | | | |
| | | | | | | | | | | | | | | | 0 | -8 | 4 | 2 | | |
| | | | | | | | | | | | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 3359375*2 |
0 | .67188*2 |
1 | .34375*2 |
0 | .6875*2 |
1 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1194684.335937510 = 100100011101010111100.01010112
answer: 123ABC.5616 = 100100011101010111100.01010112