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:
AA516 = A A 5 = A(=1010) A(=1010) 5(=0101) = 1010101001012
answer: AA516 = 1010101001012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙162+10∙161+5∙160 = 10∙256+10∙16+5∙1 = 2560+160+5 = 272510
got It: AA516 =272510
Translate the number 272510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2725 | 2 | | | | | | | | | | | |
-2724 | 1362 | 2 | | | | | | | | | | |
1 | -1362 | 681 | 2 | | | | | | | | | |
| 0 | -680 | 340 | 2 | | | | | | | | |
| | 1 | -340 | 170 | 2 | | | | | | | |
| | | 0 | -170 | 85 | 2 | | | | | | |
| | | | 0 | -84 | 42 | 2 | | | | | |
| | | | | 1 | -42 | 21 | 2 | | | | |
| | | | | | 0 | -20 | 10 | 2 | | | |
| | | | | | | 1 | -10 | 5 | 2 | | |
| | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | 0 | | |
|
the result of the conversion was:
272510 = 1010101001012
answer: AA516 = 1010101001012