# 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:

 4294967296 2 -4294967296 2147483648 2 0 -2147483648 1073741824 2 0 -1073741824 536870912 2 0 -536870912 268435456 2 0 -268435456 134217728 2 0 -134217728 67108864 2 0 -67108864 33554432 2 0 -33554432 16777216 2 0 -16777216 8388608 2 0 -8388608 4194304 2 0 -4194304 2097152 2 0 -2097152 1048576 2 0 -1048576 524288 2 0 -524288 262144 2 0 -262144 131072 2 0 -131072 65536 2 0 -65536 32768 2 0 -32768 16384 2 0 -16384 8192 2 0 -8192 4096 2 0 -4096 2048 2 0 -2048 1024 2 0 -1024 512 2 0 -512 256 2 0 -256 128 2 0 -128 64 2 0 -64 32 2 0 -32 16 2 0 -16 8 2 0 -8 4 2 0 -4 2 2 0 -2 1 0

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

 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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