This transfer is possible in two ways: direct transfer and using the decimal system.
first, let\'s make a direct transfer.
Fill in the number with missing zeros on the left
let\'s do a direct translation from binary to hexadecimal like this:
0100101100010101.110000102 = 0100 1011 0001 0101. 1100 0010 = 0100(=4) 1011(=B) 0001(=1) 0101(=5). 1100(=C) 0010(=2) = 4B15.C216
answer: 0100101100010101.110000102 = 4B15.C216
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
0∙215+1∙214+0∙213+0∙212+1∙211+0∙210+1∙29+1∙28+0∙27+0∙26+0∙25+1∙24+0∙23+1∙22+0∙21+1∙20+1∙2-1+1∙2-2+0∙2-3+0∙2-4+0∙2-5+0∙2-6+1∙2-7+0∙2-8 = 0∙32768+1∙16384+0∙8192+0∙4096+1∙2048+0∙1024+1∙512+1∙256+0∙128+0∙64+0∙32+1∙16+0∙8+1∙4+0∙2+1∙1+1∙0.5+1∙0.25+0∙0.125+0∙0.0625+0∙0.03125+0∙0.015625+1∙0.0078125+0∙0.00390625 = 0+16384+0+0+2048+0+512+256+0+0+0+16+0+4+0+1+0.5+0.25+0+0+0+0+0.0078125+0 = 19221.757812510
got It: 0100101100010101.110000102 =19221.757812510
Translate the number 19221.757812510 в hexadecimal like this:
the Integer part of the number is divided by the base of the new number system:
19221 | 16 | | | |
-19216 | 1201 | 16 | | |
5 | -1200 | 75 | 16 | |
| 1 | -64 | 4 | |
| | B | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 7578125*16 |
C | .125*16 |
2 | .0*16 |
the result of the conversion was:
19221.757812510 = 4B15.C216
answer: 0100101100010101.110000102 = 4B15.C216