# Approximating $\pi$ in Binary

I am interested in creating a Java program that generates digits of $\pi$ (in Binary though). To be clear, the number I'm looking for begins: $11.00100100 \dots$

I am unsure of the most efficient way to generate the number. I have looked at the Wikipedia page for this, and I cannot seem to tell which method would be most efficient. I am looking to generating digits of $\pi$ up to perhaps even the billionth digit, so I am looking for a method that is efficient even for such accurate approximations.

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