Transforming Gaussian random $[0,1] $ numbers to uniform $[0,255] $
There is no such thing like a Gaussian distribution over [0,1]; this doesn't make any sense. So it is not clear what you have to begin with.

However, if you have independent random values, you can generate a random bit by taking two values A and B and comparing them. E.g., if $A&lt;B$ you set the bit to 0, otherwise you set the bit to 1. A sequence of 8 such bits is then a (uniformly distributed) random byte.

PS: As correctly mentionned by Ilmari Karonen, if you have a non-negligible probability to have A=B, you have to check for this and if it happens you have to discard A and B.