Transfer 100000000.0000111 from hexadecimal in binary number system

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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:

100000000.000011116 = 1 0 0 0 0 0 0 0 0. 0 0 0 0 1 1 1 = 1(=0001) 0(=0000) 0(=0000) 0(=0000) 0(=0000) 0(=0000) 0(=0000) 0(=0000) 0(=0000). 0(=0000) 0(=0000) 0(=0000) 0(=0000) 1(=0001) 1(=0001) 1(=0001) = 100000000000000000000000000000000.00000000000000000001000100012

the Final answer: 100000000.000011116 = 100000000000000000000000000000000.00000000000000000001000100012

now let\'s make the transfer using the decimal system.

let\'s translate to decimal like this:

1∙168+0∙167+0∙166+0∙165+0∙164+0∙163+0∙162+0∙161+0∙160+0∙16-1+0∙16-2+0∙16-3+0∙16-4+1∙16-5+1∙16-6+1∙16-7 = 1∙4294967296+0∙268435456+0∙16777216+0∙1048576+0∙65536+0∙4096+0∙256+0∙16+0∙1+0∙0.0625+0∙0.00390625+0∙0.000244140625+0∙1.52587890625E-5+1∙9.5367431640625E-7+1∙5.9604644775391E-8+1∙3.7252902984619E-9 = 4294967296+0+0+0+0+0+0+0+0+0+0+0+0+9.5367431640625E-7+5.9604644775391E-8+3.7252902984619E-9 = 4294967296.1.0170042514801E-610

got It: 100000000.000011116 =4294967296.1.0170042514801E-610

Translate the number 4294967296.1.0170042514801E-610 в binary like this:

the Integer part of the number is divided by the base of the new number system:

42949672962
-429496729621474836482
0-214748364810737418242
0-10737418245368709122
0-5368709122684354562
0-2684354561342177282
0-134217728671088642
0-67108864335544322
0-33554432167772162
0-1677721683886082
0-838860841943042
0-419430420971522
0-209715210485762
0-10485765242882
0-5242882621442
0-2621441310722
0-131072655362
0-65536327682
0-32768163842
0-1638481922
0-819240962
0-409620482
0-204810242
0-10245122
0-5122562
0-2561282
0-128642
0-64322
0-32162
0-1682
0-842
0-422
0-21
0
Перевод чисел из одной системы счисления в другую

the Fractional part of the number is multiplied by the base of the new number system:

 Transferring numbers from one number system to another
0.1.0170042514801E-6*2
0.2*2
0.4*2
0.8*2
1.6*2
1.2*2
0.4*2
0.8*2
1.6*2
1.2*2
0.4*2

the result of the conversion was:

4294967296.1.0170042514801E-610 = 100000000000000000000000000000000.00011001102
the Final answer: 100000000.000011116 = 100000000000000000000000000000000.00011001102
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