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:
9ef16 = 9 e f = 9(=1001) e(=1110) f(=1111) = 1001111011112
answer: 9ef16 = 1001111011112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
9∙162+14∙161+15∙160 = 9∙256+14∙16+15∙1 = 2304+224+15 = 254310
got It: 9ef16 =254310
Translate the number 254310 в binary like this:
the Integer part of the number is divided by the base of the new number system:
2543 | 2 | | | | | | | | | | | |
-2542 | 1271 | 2 | | | | | | | | | | |
1 | -1270 | 635 | 2 | | | | | | | | | |
| 1 | -634 | 317 | 2 | | | | | | | | |
| | 1 | -316 | 158 | 2 | | | | | | | |
| | | 1 | -158 | 79 | 2 | | | | | | |
| | | | 0 | -78 | 39 | 2 | | | | | |
| | | | | 1 | -38 | 19 | 2 | | | | |
| | | | | | 1 | -18 | 9 | 2 | | | |
| | | | | | | 1 | -8 | 4 | 2 | | |
| | | | | | | | 1 | -4 | 2 | 2 | |
| | | | | | | | | 0 | -2 | 1 | |
| | | | | | | | | | 0 | | |
|
the result of the conversion was:
254310 = 1001111011112
answer: 9ef16 = 1001111011112