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:
4a.3f16 = 4 a. 3 f = 4(=0100) a(=1010). 3(=0011) f(=1111) = 1001010.001111112
answer: 4a.3f16 = 1001010.001111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
4∙161+10∙160+3∙16-1+15∙16-2 = 4∙16+10∙1+3∙0.0625+15∙0.00390625 = 64+10+0.1875+0.05859375 = 74.2460937510
got It: 4a.3f16 =74.2460937510
Translate the number 74.2460937510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
74 | 2 | | | | | | |
-74 | 37 | 2 | | | | | |
0 | -36 | 18 | 2 | | | | |
| 1 | -18 | 9 | 2 | | | |
| | 0 | -8 | 4 | 2 | | |
| | | 1 | -4 | 2 | 2 | |
| | | | 0 | -2 | 1 | |
| | | | | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 24609375*2 |
0 | .49219*2 |
0 | .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:
74.2460937510 = 1001010.001111112
answer: 4a.3f16 = 1001010.001111112