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

Simple place value. In base 10, you have these places:

... 10³ 10² 10¹ 10⁰ . 10^-1 10^-2 10^-3 ...

... thousands, hundreds, tens, ones . tenths, hundredths, thousandths ...

Similarly, in binary (base 2) you have:

... 2³ 2² 2¹ 2⁰ . 2^-1 2^-2 2^-3 ...

... eights, fours, twos, ones . halves, quarters, eighths ...

So the second place after the . in binary is units of 2^-2, well known to you as units of 1/4 (or alternately, 0.25).