Question

Similar to decimal binary numbers can have represent floats too. Now I read that it can have floats of the sort

0.5:0.1 , 0.25:0.01 , 0.125:0.001 … and so on. But then, for example, how is the 0.1(in decimal) represented in binary?

Also, given a decimal float, how to convert it to the decimal equivalent, (given it is not so straightforward).

Edit: So I understand that the better question would have been ; how to convert a decimal float to binary? Now i get it that we multiply the decimal part, till it becomes zero.
Now it is very much possible that two floating points can have the same representation right?

Answer 1

Given how many bits?

0.1b:

0.00011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011...

As you can see it’s an approximation.

Binary                                          Decimal
0.1     == 1/2^1         == 1/2              == 0.5
0.01    == 1/2^2         == 1/4              == 0.25
0.11    == 1/2^1 + 1/2^2 == 1/2 + 1/4 == 3/4 == 0.75

Each bit after the radix point represents 1/2^(position_after_bit_string).

postion:   |1|2|3|4|5|6|7|
         0.|0|0|0|0|0|0|1|

So 0.0000001 = 1/2^7 = 0.0078125

Pseudocode:

decimal_value = 0 
for i, bit in enumerate(binary_string):
    if bit == 1
         decimal_value += 1/2**i

For more info Why can't decimal numbers be represented exactly in binary?