Java 8, 101 bytes

n->{String s=n.toString(n,2);return(s.charAt(s.length()-1)+s.replaceAll(".$","")).replace("0","-1");}

Port of @Oliver's Japt answer, with a few more bytes.. ;)

Can definitely be golfed by using an mathematical approach instead of this String approach.

Explanation:

Try it here.

n->{                             // Method with Integer parameter and String return-type
  String s=n.toString(n,2);      //  Convert the Integer to a binary String
  return(s.charAt(s.length()-1)  //  Get the last character of the binary String
    +s.replaceAll(".$","")       //   + everything except the last character
   ).replace("0","-1");          //  Then replace all zeroes with -1, and return the result
}                                // End of method