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:
12.3A16 = 1 2. 3 A = 1(=0001) 2(=0010). 3(=0011) A(=1010) = 10010.00111012
answer: 12.3A16 = 10010.00111012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
1∙161+2∙160+3∙16-1+10∙16-2 = 1∙16+2∙1+3∙0.0625+10∙0.00390625 = 16+2+0.1875+0.0390625 = 18.226562510
got It: 12.3A16 =18.226562510
Translate the number 18.226562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
18 | 2 | | | | |
-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. | 2265625*2 |
0 | .45313*2 |
0 | .90625*2 |
1 | .8125*2 |
1 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
18.226562510 = 10010.00111012
answer: 12.3A16 = 10010.00111012