Binary number

2.35 = 2+0.25+0.1

2 and 0.25 can be easily expressed in binary form, so let's consider 0.1

we have 0.1 = 0.000abcde......
so we magnify it to 0.8
0.8 = 0.abcd....

Now notice that the fact that 1100 base 2 is 80% of 1111.
So when the cyclic period is 4, 0.8 would be 0.110011001100......
=> 0.1 = 0.00011001100...
2.35 base 10
= 10 + 0.01 + 0.00011001100... base 2
= 10.010110011001100.....

2 = 10(2)

0.35 x 2 = 0.7 .......0
0.7 x 2 = 1.4 .........1

0.4 x 2 = 0.8 .........0
0.8 x 2 = 1.6 .........1
0.6 x 2 = 1.2 .........1
0.2 x 2 = 0.4 .........0

0.4 x 2 = 0.8 .........0

So

0.35 = 0 . 01 0110 0110 0110 ..... (2)

2.35 = 10 . 01 0110 0110 0110 ..... (2)