"Fixed point" binary sequence for values between 0 and 1

I want to express the values between 0 and 1 as binary sequences of the form

Currently, I've been converting my float to the IEEE bits and extracting the fractional part. However, this requires me to analyze the exponential part to see how many "0 placeholders" I need to add in.

Is there a way to go from float to fixed point binary sequence?

Forgive me if any terminology is confusing, I am just beginning to study CS stuff.

Answer 1

[Chunru]

% Given x in [0, 1)
x = 0.5234567

x = 0.5235

% Number of bits in binary (bits after .)
n = 32;
b = dec2bin(x*2.^n, n);
b=['0.' b]

b = '0.10000110000000010100001000011111'