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:
67E.7A16 = 6 7 E. 7 A = 6(=0110) 7(=0111) E(=1110). 7(=0111) A(=1010) = 11001111110.01111012
answer: 67E.7A16 = 11001111110.01111012
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
6∙162+7∙161+14∙160+7∙16-1+10∙16-2 = 6∙256+7∙16+14∙1+7∙0.0625+10∙0.00390625 = 1536+112+14+0.4375+0.0390625 = 1662.476562510
got It: 67E.7A16 =1662.476562510
Translate the number 1662.476562510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
1662 | 2 | | | | | | | | | | |
-1662 | 831 | 2 | | | | | | | | | |
0 | -830 | 415 | 2 | | | | | | | | |
| 1 | -414 | 207 | 2 | | | | | | | |
| | 1 | -206 | 103 | 2 | | | | | | |
| | | 1 | -102 | 51 | 2 | | | | | |
| | | | 1 | -50 | 25 | 2 | | | | |
| | | | | 1 | -24 | 12 | 2 | | | |
| | | | | | 1 | -12 | 6 | 2 | | |
| | | | | | | 0 | -6 | 3 | 2 | |
| | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 4765625*2 |
0 | .95313*2 |
1 | .90625*2 |
1 | .8125*2 |
1 | .625*2 |
1 | .25*2 |
0 | .5*2 |
1 | .0*2 |
the result of the conversion was:
1662.476562510 = 11001111110.01111012
answer: 67E.7A16 = 11001111110.01111012