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:
23F16 = 2 3 F = 2(=0010) 3(=0011) F(=1111) = 10001111112
answer: 23F16 = 10001111112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
2∙162+3∙161+15∙160 = 2∙256+3∙16+15∙1 = 512+48+15 = 57510
got It: 23F16 =57510
Translate the number 57510 в binary like this:
the Integer part of the number is divided by the base of the new number system:
575 | 2 | | | | | | | | | |
-574 | 287 | 2 | | | | | | | | |
1 | -286 | 143 | 2 | | | | | | | |
| 1 | -142 | 71 | 2 | | | | | | |
| | 1 | -70 | 35 | 2 | | | | | |
| | | 1 | -34 | 17 | 2 | | | | |
| | | | 1 | -16 | 8 | 2 | | | |
| | | | | 1 | -8 | 4 | 2 | | |
| | | | | | 0 | -4 | 2 | 2 | |
| | | | | | | 0 | -2 | 1 | |
| | | | | | | | 0 | | |
|
the result of the conversion was:
57510 = 10001111112
answer: 23F16 = 10001111112