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:
101010101016 = 1 0 1 0 1 0 1 0 1 0 = 1(=0001) 0(=0000) 1(=0001) 0(=0000) 1(=0001) 0(=0000) 1(=0001) 0(=0000) 1(=0001) 0(=0000) = 10000000100000001000000010000000100002
answer: 101010101016 = 10000000100000001000000010000000100002
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙169+0∙168+1∙167+0∙166+1∙165+0∙164+1∙163+0∙162+1∙161+0∙160 = 1∙68719476736+0∙4294967296+1∙268435456+0∙16777216+1∙1048576+0∙65536+1∙4096+0∙256+1∙16+0∙1 = 68719476736+0+268435456+0+1048576+0+4096+0+16+0 = 6898896488010
got It: 101010101016 =6898896488010
Translate the number 6898896488010 в binary like this:
the Integer part of the number is divided by the base of the new number system:
68988964880 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
-68988964880 | 34494482440 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
0 | -34494482440 | 17247241220 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 0 | -17247241220 | 8623620610 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 0 | -8623620610 | 4311810305 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 0 | -4311810304 | 2155905152 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 1 | -2155905152 | 1077952576 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 0 | -1077952576 | 538976288 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 0 | -538976288 | 269488144 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | 0 | -269488144 | 134744072 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 0 | -134744072 | 67372036 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 0 | -67372036 | 33686018 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | 0 | -33686018 | 16843009 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 0 | -16843008 | 8421504 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 1 | -8421504 | 4210752 | 2 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 0 | -4210752 | 2105376 | 2 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 0 | -2105376 | 1052688 | 2 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 0 | -1052688 | 526344 | 2 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 0 | -526344 | 263172 | 2 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 0 | -263172 | 131586 | 2 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 0 | -131586 | 65793 | 2 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 0 | -65792 | 32896 | 2 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 1 | -32896 | 16448 | 2 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 0 | -16448 | 8224 | 2 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 0 | -8224 | 4112 | 2 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 0 | -4112 | 2056 | 2 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 0 | -2056 | 1028 | 2 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 0 | -1028 | 514 | 2 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -514 | 257 | 2 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -256 | 128 | 2 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -128 | 64 | 2 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -64 | 32 | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -32 | 16 | 2 | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -16 | 8 | 2 | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -8 | 4 | 2 | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | | |
|
the result of the conversion was:
6898896488010 = 10000000100000001000000010000000100002
answer: 101010101016 = 10000000100000001000000010000000100002