Bianry to polynomial conversion

[Rubik]

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?

 

[eumyang]

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,
$$D_{16} = 1101_2 = x^3 + x^2 + 1$$
?
(Assuming the binary number was written MS bit-first.)

 

[HallsofIvy]

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.

 

[Ivan92]

Are you talking about binary representations of floating-points?

 

[CellCoree]

Converting binary into polynomial form involves representing the binary digits as coefficients of a polynomial expression. To do this, we first need to understand the relationship between binary and polynomial representations.

In binary, each digit can only have two possible values, 0 or 1. This is similar to the coefficients in a polynomial, where each term can only have two possible values, 0 or 1. For example, the binary number 01001000 can be thought of as the polynomial expression 0x^7 + 1x^6 + 0x^5 + 0x^4 + 1x^3 + 0x^2 + 0x + 0.

To convert a binary number into polynomial form, we follow these steps:

1. Write the binary number in expanded form, with each digit representing a power of 2. For example, the binary number 01001000 can be written as 0x^7 + 1x^6 + 0x^5 + 0x^4 + 1x^3 + 0x^2 + 0x + 0.

2. Simplify the expression by removing any terms with a coefficient of 0. In our example, the expression simplifies to 1x^6 + 1x^3.

3. Replace all instances of x with the variable of your choice. In this case, we can use x or any other letter as the variable.

4. Combine like terms to get the final polynomial expression. In our example, the final polynomial form would be x^6 + x^3.

In summary, converting binary into polynomial form involves representing the binary digits as coefficients of a polynomial expression, simplifying the expression, and combining like terms to get the final polynomial form.