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:
Face1616 = F a c e 1 6 = F(=1111) a(=1010) c(=1100) e(=1110) 1(=0001) 6(=0110) = 1111101011001110000101102
answer: Face1616 = 1111101011001110000101102
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙165+10∙164+12∙163+14∙162+1∙161+6∙160 = 15∙1048576+10∙65536+12∙4096+14∙256+1∙16+6∙1 = 15728640+655360+49152+3584+16+6 = 1643675810
got It: Face1616 =1643675810
Translate the number 1643675810 в binary like this:
the Integer part of the number is divided by the base of the new number system:
16436758 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
-16436758 | 8218379 | 2 | | | | | | | | | | | | | | | | | | | | | | |
0 | -8218378 | 4109189 | 2 | | | | | | | | | | | | | | | | | | | | | |
| 1 | -4109188 | 2054594 | 2 | | | | | | | | | | | | | | | | | | | | |
| | 1 | -2054594 | 1027297 | 2 | | | | | | | | | | | | | | | | | | | |
| | | 0 | -1027296 | 513648 | 2 | | | | | | | | | | | | | | | | | | |
| | | | 1 | -513648 | 256824 | 2 | | | | | | | | | | | | | | | | | |
| | | | | 0 | -256824 | 128412 | 2 | | | | | | | | | | | | | | | | |
| | | | | | 0 | -128412 | 64206 | 2 | | | | | | | | | | | | | | | |
| | | | | | | 0 | -64206 | 32103 | 2 | | | | | | | | | | | | | | |
| | | | | | | | 0 | -32102 | 16051 | 2 | | | | | | | | | | | | | |
| | | | | | | | | 1 | -16050 | 8025 | 2 | | | | | | | | | | | | |
| | | | | | | | | | 1 | -8024 | 4012 | 2 | | | | | | | | | | | |
| | | | | | | | | | | 1 | -4012 | 2006 | 2 | | | | | | | | | | |
| | | | | | | | | | | | 0 | -2006 | 1003 | 2 | | | | | | | | | |
| | | | | | | | | | | | | 0 | -1002 | 501 | 2 | | | | | | | | |
| | | | | | | | | | | | | | 1 | -500 | 250 | 2 | | | | | | | |
| | | | | | | | | | | | | | | 1 | -250 | 125 | 2 | | | | | | |
| | | | | | | | | | | | | | | | 0 | -124 | 62 | 2 | | | | | |
| | | | | | | | | | | | | | | | | 1 | -62 | 31 | 2 | | | | |
| | | | | | | | | | | | | | | | | | 0 | -30 | 15 | 2 | | | |
| | | | | | | | | | | | | | | | | | | 1 | -14 | 7 | 2 | | |
| | | | | | | | | | | | | | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | 1 | | |
|
the result of the conversion was:
1643675810 = 1111101011001110000101102
answer: Face1616 = 1111101011001110000101102