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:
6D.4CCCCCCCCC16 = 6 D. 4 C C C C C C C C C = 6(=0110) D(=1101). 4(=0100) C(=1100) C(=1100) C(=1100) C(=1100) C(=1100) C(=1100) C(=1100) C(=1100) C(=1100) = 1101101.010011001100110011001100110011001100112
answer: 6D.4CCCCCCCCC16 = 1101101.010011001100110011001100110011001100112
now let\'s make the transfer using the decimal system.
let\'s translate to decimal like this:
6∙161+13∙160+4∙16-1+12∙16-2+12∙16-3+12∙16-4+12∙16-5+12∙16-6+12∙16-7+12∙16-8+12∙16-9+12∙16-10 = 6∙16+13∙1+4∙0.0625+12∙0.00390625+12∙0.000244140625+12∙1.52587890625E-5+12∙9.5367431640625E-7+12∙5.9604644775391E-8+12∙3.7252902984619E-9+12∙2.3283064365387E-10+12∙1.4551915228367E-11+12∙9.0949470177293E-13 = 96+13+0.25+0.046875+0.0029296875+0.00018310546875+1.1444091796875E-5+7.1525573730469E-7+4.4703483581543E-8+2.7939677238464E-9+1.746229827404E-10+1.0913936421275E-11 = 109.2999999999992710
got It: 6D.4CCCCCCCCC16 =109.2999999999992710
Translate the number 109.2999999999992710 в binary like this:
the Integer part of the number is divided by the base of the new number system:
109 | 2 | | | | | | |
-108 | 54 | 2 | | | | | |
1 | -54 | 27 | 2 | | | | |
| 0 | -26 | 13 | 2 | | | |
| | 1 | -12 | 6 | 2 | | |
| | | 1 | -6 | 3 | 2 | |
| | | | 0 | -2 | 1 | |
| | | | | 1 | | |
|
the Fractional part of the number is multiplied by the base of the new number system:
|
0. | 29999999999927*2 |
0 | .6*2 |
1 | .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 |
the result of the conversion was:
109.2999999999992710 = 1101101.01001100112
answer: 6D.4CCCCCCCCC16 = 1101101.01001100112