FFT of random binary data
I had a similar question myself, so I created a html demo to test this. 

I think you may find it useful in understanding what the FFT is actually doing since you can also read and edit the source code.

https://seanwasere.gitlab.io/FFTBinary



This demo is doing FFT analysis of binary data. 1s and 0s

In my demo I have 1024 bits, and I convert them into an 8 bit wav, and then analyse it using the browsers inbuilt audio api fft analysis function. Firefox browser works best in my case.

The 8 bit wav is 


1 channel 
samplerate 48000
1024 bits = 0.021333333333333332 seconds in length
the 1s and 0s are actually converted behind the scenes to 256s and 128s


In the user interface there are 4 panels


1st is the FFT result of the binary data drawn as a spectrum graph,
2nd is the FFT result drawn as a waveform. It is essentially triangular spikes or squares, depending on the sequence 0,1,0 or 0,1,1,0.
3rd panel is a view of the actual binary data that was converted into the waveform before FFT analysis.
4th panel is your options, you can 


set to have a '1' every N bits by using modulus, 
and/or play random 1s and 0s which I call binary white noise.
set the FFT buffer size, the lower numbers such as 128 give lower quality output but is much faster to compute.



The source code is MIT so you can play around with it.