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:
2CB.7F16 = 2 C B. 7 F = 2(=0010) C(=1100) B(=1011). 7(=0111) F(=1111) = 1011001011.011111112
answer: 2CB.7F16 = 1011001011.011111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
2∙162+12∙161+11∙160+7∙16-1+15∙16-2 = 2∙256+12∙16+11∙1+7∙0.0625+15∙0.00390625 = 512+192+11+0.4375+0.05859375 = 715.4960937510
got It: 2CB.7F16 =715.4960937510
Translate the number 715.4960937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
715 | 2 | | | | | | | | | |
-714 | 357 | 2 | | | | | | | | |
1 | -356 | 178 | 2 | | | | | | | |
| 1 | -178 | 89 | 2 | | | | | | |
| | 0 | -88 | 44 | 2 | | | | | |
| | | 1 | -44 | 22 | 2 | | | | |
| | | | 0 | -22 | 11 | 2 | | | |
| | | | | 0 | -10 | 5 | 2 | | |
| | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | 1 | -2 | 1 | |
| | | | | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 49609375*2 |
0 | .99219*2 |
1 | .98438*2 |
1 | .96875*2 |
1 | .9375*2 |
1 | .875*2 |
1 | .75*2 |
1 | .5*2 |
1 | .0*2 |
the result of the conversion was:
715.4960937510 = 1011001011.011111112
answer: 2CB.7F16 = 1011001011.011111112