How can I truncate the fractional part of a number in base 2?

Questions
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1

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.

2

Try to use RealDigits:

RealDigits[fp, 2, 8, -1][[1]]

this gives a list of numbers, you could use ToString and StringJoin to make a complete string.

here is a working example:

GiveMeRealDigitsBehindCommaString[number_,base_,length_]:="0."<>StringJoin[ToString/@RealDigits[FractionalPart[number],base,length,-1][[1]]]
GiveMeRealDigitsBehindCommaString[N[\[Pi]],2,8]

this will return:
“0.00100100” (as a string)