In binary notation, what is the meaning of the digits after the radix point “.”?

Question

I have this example on how to convert from a base 10 number to IEEE 754 float representation

Number: 45.25 (base 10) = 101101.01 (base 2) Sign: 0
Normalized          


        

Answer 1

You can think of 0.25 as 1/4.

Dividing by 2 in (base 2) moves the decimal point one step left, the same way dividing by 10 in (base 10) moves the decimal point one step left. Generally dividing by M in (base M) moves the decimal point one step left.

so

base 10                  base 2
--------------------------------------
1                      =>      1
1/2 = 0.5              =>    0.1
0.5/2 = 1/4 = 0.25     =>   0.01 
0.25/2 = 1/8 = 0.125   =>  0.001
.
.
.

etc.