Bianry to polynomial conversion

  • Context: Undergrad 
  • Thread starter Thread starter Rubik
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    Polynomial
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Discussion Overview

The discussion focuses on the conversion of binary numbers into polynomial form, exploring the relationship between binary representations and polynomial expressions. Participants consider different contexts, including finite fields and potential applications to floating-point representations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant asks how to convert binary into polynomial form, referencing their understanding of hexadecimal conversion.
  • Another participant suggests that if polynomials over GF(2) are being discussed, each bit can be assigned as a coefficient of a power of x, providing an example of a binary number converted to polynomial form.
  • A different participant challenges the notion of converting binary to polynomial, stating that numbers are not polynomials without a clear association method.
  • One participant questions whether the discussion pertains to binary representations of floating-point numbers.

Areas of Agreement / Disagreement

Participants express differing views on the conversion process and the context in which binary numbers are being considered, indicating that multiple competing views remain without consensus.

Contextual Notes

There are unresolved assumptions regarding the definitions of polynomials and the specific context of binary representation, such as whether it pertains to finite fields or floating-point numbers.

Rubik
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How do you convert binary into polynomial form? I understand hexadecial conversion so {4e} = 01001000 now how do I go about changing that into a polynomial?
 
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When you're talking about polynomials, you're referring to polynomials over GF(2)? If so, isn't it just a matter of assigning each bit as a coefficient of a power of x (or whatever variable)? For instance,
[tex]D_{16} = 1101_2 = x^3 + x^2 + 1[/tex]
?
(Assuming the binary number was written MS bit-first.)
 
Rubik said:
How do you convert binary into polynomial form? I understand hexadecial conversion so {4e} = 01001000 now how do I go about changing that into a polynomial?
Numbers are NOT polynomials so you don't- not without saying exactly how you are associating each number with a specific polynomial as eumyang says.
 
Are you talking about binary representations of floating-points?
 

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