Weird Calculator

Lynn has a calculator with only two buttons that perform +1\boxed{+1} and ÷2\boxed{\div 2}.

She also has a screen with 99 significant figures, and it displays 00 when she gets the calculator.

If she wants to display π\pi up to the eighth decimal (3.14159265)(3.14159265), what is the fewest number of taps she needs to do?

Hint: The first 64 bits of π\pi in binary are given below:

π\pi \approx11.001001000011111101101010100010001000010110100011000010001101002_2

Note: You may want to use the code environment below.


        

        
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