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:
CAFE1616 = C A F E 1 6 = C(=1100) A(=1010) F(=1111) E(=1110) 1(=0001) 6(=0110) = 1100101011111110000101102
answer: CAFE1616 = 1100101011111110000101102
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
12∙165+10∙164+15∙163+14∙162+1∙161+6∙160 = 12∙1048576+10∙65536+15∙4096+14∙256+1∙16+6∙1 = 12582912+655360+61440+3584+16+6 = 1330331810
got It: CAFE1616 =1330331810
Translate the number 1330331810 в binary like this:
the Integer part of the number is divided by the base of the new number system:
13303318 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
-13303318 | 6651659 | 2 | | | | | | | | | | | | | | | | | | | | | | |
0 | -6651658 | 3325829 | 2 | | | | | | | | | | | | | | | | | | | | | |
| 1 | -3325828 | 1662914 | 2 | | | | | | | | | | | | | | | | | | | | |
| | 1 | -1662914 | 831457 | 2 | | | | | | | | | | | | | | | | | | | |
| | | 0 | -831456 | 415728 | 2 | | | | | | | | | | | | | | | | | | |
| | | | 1 | -415728 | 207864 | 2 | | | | | | | | | | | | | | | | | |
| | | | | 0 | -207864 | 103932 | 2 | | | | | | | | | | | | | | | | |
| | | | | | 0 | -103932 | 51966 | 2 | | | | | | | | | | | | | | | |
| | | | | | | 0 | -51966 | 25983 | 2 | | | | | | | | | | | | | | |
| | | | | | | | 0 | -25982 | 12991 | 2 | | | | | | | | | | | | | |
| | | | | | | | | 1 | -12990 | 6495 | 2 | | | | | | | | | | | | |
| | | | | | | | | | 1 | -6494 | 3247 | 2 | | | | | | | | | | | |
| | | | | | | | | | | 1 | -3246 | 1623 | 2 | | | | | | | | | | |
| | | | | | | | | | | | 1 | -1622 | 811 | 2 | | | | | | | | | |
| | | | | | | | | | | | | 1 | -810 | 405 | 2 | | | | | | | | |
| | | | | | | | | | | | | | 1 | -404 | 202 | 2 | | | | | | | |
| | | | | | | | | | | | | | | 1 | -202 | 101 | 2 | | | | | | |
| | | | | | | | | | | | | | | | 0 | -100 | 50 | 2 | | | | | |
| | | | | | | | | | | | | | | | | 1 | -50 | 25 | 2 | | | | |
| | | | | | | | | | | | | | | | | | 0 | -24 | 12 | 2 | | | |
| | | | | | | | | | | | | | | | | | | 1 | -12 | 6 | 2 | | |
| | | | | | | | | | | | | | | | | | | | 0 | -6 | 3 | 2 | |
| | | | | | | | | | | | | | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | 1 | | |
|
the result of the conversion was:
1330331810 = 1100101011111110000101102
answer: CAFE1616 = 1100101011111110000101102