Transfer 7753.1004 from octal 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 octal to binary like this:

7753.10048 = 7 7 5 3. 1 0 0 4 = 7(=111) 7(=111) 5(=101) 3(=011). 1(=001) 0(=000) 0(=000) 4(=100) = 111111101011.0010000001002

the Final answer: 7753.10048 = 111111101011.00100000012

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

let's translate to decimal like this:

7∙83+7∙82+5∙81+3∙80+1∙8-1+0∙8-2+0∙8-3+4∙8-4 = 7∙512+7∙64+5∙8+3∙1+1∙0.125+0∙0.015625+0∙0.001953125+4∙0.000244140625 = 3584+448+40+3+0.125+0+0+0.0009765625 = 4075.125976562510

got It: 7753.10048 =4075.125976562510

Translate the number 4075.125976562510 в binary like this:

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

40752
-407420372
1-203610182
1-10185092
0-5082542
1-2541272
0-126632
1-62312
1-30152
1-1472
1-632
1-21
1
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
0.1259765625*2
0.25195*2
0.50391*2
1.00781*2
0.01563*2
0.03125*2
0.0625*2
0.125*2
0.25*2
0.5*2
1.0*2

the result of the conversion was:

4075.125976562510 = 111111101011.00100000012
the Final answer: 7753.10048 = 111111101011.00100000012

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