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:
A2DF16 = A 2 D F = A(=1010) 2(=0010) D(=1101) F(=1111) = 10100010110111112
answer: A2DF16 = 10100010110111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙163+2∙162+13∙161+15∙160 = 10∙4096+2∙256+13∙16+15∙1 = 40960+512+208+15 = 4169510
got It: A2DF16 =4169510
Translate the number 4169510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
41695 | 2 | | | | | | | | | | | | | | | |
-41694 | 20847 | 2 | | | | | | | | | | | | | | |
1 | -20846 | 10423 | 2 | | | | | | | | | | | | | |
| 1 | -10422 | 5211 | 2 | | | | | | | | | | | | |
| | 1 | -5210 | 2605 | 2 | | | | | | | | | | | |
| | | 1 | -2604 | 1302 | 2 | | | | | | | | | | |
| | | | 1 | -1302 | 651 | 2 | | | | | | | | | |
| | | | | 0 | -650 | 325 | 2 | | | | | | | | |
| | | | | | 1 | -324 | 162 | 2 | | | | | | | |
| | | | | | | 1 | -162 | 81 | 2 | | | | | | |
| | | | | | | | 0 | -80 | 40 | 2 | | | | | |
| | | | | | | | | 1 | -40 | 20 | 2 | | | | |
| | | | | | | | | | 0 | -20 | 10 | 2 | | | |
| | | | | | | | | | | 0 | -10 | 5 | 2 | | |
| | | | | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | 0 | | |
|
the result of the conversion was:
4169510 = 10100010110111112
answer: A2DF16 = 10100010110111112