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If I have a fractional value, how can I truncate (not round) that to a certain number of bits, like 8?

For example, for Pi 3.141569265359... the fractional part is 0.141569265359...

NumberForm[BaseForm[FractionalPart[N[Pi]],2],8]

0.00100100001111110110101010001

But this is giving me 8 decimal digits of PI in base 2. What I want is 8 binary digits in base 2.

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NumberForm is for representation purposes only. I suggest you use RealDigits, and then take the number of bits you need from its first returned element or, better yet

Rest[ First[ RealDigits[FractionalPart[N[Pi]], 2, 8+1]]]

EDIT: corrected to give only the bits needed.

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