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:
FFFAAA16 = F F F A A A = F(=1111) F(=1111) F(=1111) A(=1010) A(=1010) A(=1010) = 1111111111111010101010102
answer: FFFAAA16 = 1111111111111010101010102
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
15∙165+15∙164+15∙163+10∙162+10∙161+10∙160 = 15∙1048576+15∙65536+15∙4096+10∙256+10∙16+10∙1 = 15728640+983040+61440+2560+160+10 = 1677585010
got It: FFFAAA16 =1677585010
Translate the number 1677585010 в binary like this:
the Integer part of the number is divided by the base of the new number system:
16775850 | 2 | | | | | | | | | | | | | | | | | | | | | | | |
-16775850 | 8387925 | 2 | | | | | | | | | | | | | | | | | | | | | | |
0 | -8387924 | 4193962 | 2 | | | | | | | | | | | | | | | | | | | | | |
| 1 | -4193962 | 2096981 | 2 | | | | | | | | | | | | | | | | | | | | |
| | 0 | -2096980 | 1048490 | 2 | | | | | | | | | | | | | | | | | | | |
| | | 1 | -1048490 | 524245 | 2 | | | | | | | | | | | | | | | | | | |
| | | | 0 | -524244 | 262122 | 2 | | | | | | | | | | | | | | | | | |
| | | | | 1 | -262122 | 131061 | 2 | | | | | | | | | | | | | | | | |
| | | | | | 0 | -131060 | 65530 | 2 | | | | | | | | | | | | | | | |
| | | | | | | 1 | -65530 | 32765 | 2 | | | | | | | | | | | | | | |
| | | | | | | | 0 | -32764 | 16382 | 2 | | | | | | | | | | | | | |
| | | | | | | | | 1 | -16382 | 8191 | 2 | | | | | | | | | | | | |
| | | | | | | | | | 0 | -8190 | 4095 | 2 | | | | | | | | | | | |
| | | | | | | | | | | 1 | -4094 | 2047 | 2 | | | | | | | | | | |
| | | | | | | | | | | | 1 | -2046 | 1023 | 2 | | | | | | | | | |
| | | | | | | | | | | | | 1 | -1022 | 511 | 2 | | | | | | | | |
| | | | | | | | | | | | | | 1 | -510 | 255 | 2 | | | | | | | |
| | | | | | | | | | | | | | | 1 | -254 | 127 | 2 | | | | | | |
| | | | | | | | | | | | | | | | 1 | -126 | 63 | 2 | | | | | |
| | | | | | | | | | | | | | | | | 1 | -62 | 31 | 2 | | | | |
| | | | | | | | | | | | | | | | | | 1 | -30 | 15 | 2 | | | |
| | | | | | | | | | | | | | | | | | | 1 | -14 | 7 | 2 | | |
| | | | | | | | | | | | | | | | | | | | 1 | -6 | 3 | 2 | |
| | | | | | | | | | | | | | | | | | | | | 1 | -2 | 1 | |
| | | | | | | | | | | | | | | | | | | | | | 1 | | |
|
the result of the conversion was:
1677585010 = 1111111111111010101010102
answer: FFFAAA16 = 1111111111111010101010102