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:
AC1.3016 = A C 1. 3 0 = A(=1010) C(=1100) 1(=0001). 3(=0011) 0(=0000) = 101011000001.00112
answer: AC1.3016 = 101011000001.00112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙162+12∙161+1∙160+3∙16-1+0∙16-2 = 10∙256+12∙16+1∙1+3∙0.0625+0∙0.00390625 = 2560+192+1+0.1875+0 = 2753.187510
got It: AC1.3016 =2753.187510
Translate the number 2753.187510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2753 | 2 | | | | | | | | | | | |
-2752 | 1376 | 2 | | | | | | | | | | |
1 | -1376 | 688 | 2 | | | | | | | | | |
| 0 | -688 | 344 | 2 | | | | | | | | |
| | 0 | -344 | 172 | 2 | | | | | | | |
| | | 0 | -172 | 86 | 2 | | | | | | |
| | | | 0 | -86 | 43 | 2 | | | | | |
| | | | | 0 | -42 | 21 | 2 | | | | |
| | | | | | 1 | -20 | 10 | 2 | | | |
| | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 1875*2 |
0 | .375*2 |
0 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
2753.187510 = 101011000001.00112
answer: AC1.3016 = 101011000001.00112