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:
DECADE2116 = D E C A D E 2 1 = D(=1101) E(=1110) C(=1100) A(=1010) D(=1101) E(=1110) 2(=0010) 1(=0001) = 110111101100101011011110001000012
answer: DECADE2116 = 110111101100101011011110001000012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
13∙167+14∙166+12∙165+10∙164+13∙163+14∙162+2∙161+1∙160 = 13∙268435456+14∙16777216+12∙1048576+10∙65536+13∙4096+14∙256+2∙16+1∙1 = 3489660928+234881024+12582912+655360+53248+3584+32+1 = 373783708910
got It: DECADE2116 =373783708910
Translate the number 373783708910 в binary like this:
the Integer part of the number is divided by the base of the new number system:
3737837089 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
-3737837088 | 1868918544 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1 | -1868918544 | 934459272 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 0 | -934459272 | 467229636 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | 0 | -467229636 | 233614818 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | 0 | -233614818 | 116807409 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | 0 | -116807408 | 58403704 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | 1 | -58403704 | 29201852 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | 0 | -29201852 | 14600926 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | 0 | -14600926 | 7300463 | 2 | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 0 | -7300462 | 3650231 | 2 | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 1 | -3650230 | 1825115 | 2 | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | 1 | -1825114 | 912557 | 2 | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 1 | -912556 | 456278 | 2 | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 1 | -456278 | 228139 | 2 | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 0 | -228138 | 114069 | 2 | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 1 | -114068 | 57034 | 2 | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 1 | -57034 | 28517 | 2 | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 0 | -28516 | 14258 | 2 | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 1 | -14258 | 7129 | 2 | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 0 | -7128 | 3564 | 2 | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 1 | -3564 | 1782 | 2 | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 0 | -1782 | 891 | 2 | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 0 | -890 | 445 | 2 | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 1 | -444 | 222 | 2 | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 1 | -222 | 111 | 2 | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 0 | -110 | 55 | 2 | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 1 | -54 | 27 | 2 | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -26 | 13 | 2 | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -12 | 6 | 2 | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | | |
|
the result of the conversion was:
373783708910 = 110111101100101011011110001000012
answer: DECADE2116 = 110111101100101011011110001000012