[tpxl]

You can generally turn any random binary distribution into a uniform binary distribution by generating two bits, then if they're different, output the first bit, and if they're the same, ignore the result.

[londons_explore]

01 01 01 01 00 01 01 01 11 01

Doesn't seem to work... It depends on odd bits and even bits having the same distribution, which in many cases they won't.

[MauranKilom]

Yes, the draws from the random distribution must be uncorrelated. But the mentioned algorithm does indeed a "flat" output in this case.