Convert Negative Integers into Signed Binary?

Question

I'm relatively new to Mathematica and have been struggling with this problem for several days.

I have a string of integer data, ranging from -2044 to 2044. So this looks something like {-2044,-2040,-2032......2037,2040,2044} (there is no pattern in the data).

However, now I need to export this string of data to a text file in Signed binary representation.

There is a convenient way to convert positive base ten integers into binary with BaseForm, but I cannot find a way to convert negative base ten integers into Signed binary.

If anyone has any tips on how to do that, I'd appreciate the help! Thanks.

Answer 1

You can implement it easily:

Clear[signedBinary]
signedBinary[bits_][x_] := 
 IntegerDigits[Mod[x + 2^bits, 2^bits], 2, bits]

signedBinary[8] /@ {-1, 0, 10, 127}
(* {{1, 1, 1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 0}, 
    {0, 0, 0, 0, 1, 0, 1, 0}, {0, 1, 1, 1, 1, 1, 1, 1}} *)

Of course, the number of bits is important and needs to be specified. In your implementation, you may want to include a check for out-of-range numbers.

To also convert to a string,

StringJoin@*Map[ToString]@*signedBinary[8] /@ {-1, 0, 10, 127}

@* means Composition.