What is the difference between the von Neumann and Peres algorithms?



I understand that both algorithms are used to remove bias/create fair randomization from a biased source. I am confused about what the Peres algorithm is adding to the von Neumann one. What does the Peres algorithm add on and when would using it be more beneficial?

In: Mathematics

The Peres extractor just uses more of the data that the von Neumann throws away.

If the two consecutive bits are not different in the von Neumann extractor, then the algorithm just throws those two bits away and ignores them. The Peres extractor takes them and saves them for later to be reused in a manner that still preserves the 50-50 randomness we desire.

So the Peres extractor is preferable when we want to extract form 50-50 random data, but takes more time to run.