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

She also has a screen with \(9\) significant figures, and it displays \(0\) when she gets the calculator.

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

**Hint**: The first 64 bits of \(\pi\) in binary are given below:

\(\pi \approx\)`11.00100100001111110110101010001000100001011010001100001000110100`

\(_2\)

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

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