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:
A.7516 = A. 7 5 = A(=1010). 7(=0111) 5(=0101) = 1010.011101012
answer: A.7516 = 1010.011101012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
10∙160+7∙16-1+5∙16-2 = 10∙1+7∙0.0625+5∙0.00390625 = 10+0.4375+0.01953125 = 10.4570312510
got It: A.7516 =10.4570312510
Translate the number 10.4570312510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
10 | 2 | | | |
-10 | 5 | 2 | | |
0 | -4 | 2 | 2 | |
| 1 | -2 | 1 | |
| | 0 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 45703125*2 |
0 | .91406*2 |
1 | .82813*2 |
1 | .65625*2 |
1 | .3125*2 |
0 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
10.4570312510 = 1010.011101012
answer: A.7516 = 1010.011101012