One possible answer would be to "shift" the whole thing to the left—000...0 would represent the smallest number in the interval, namely -2 n, and 111...1 would represent the largest, namely 2 n-1; 0 would be represented by 100...0 somewhere in the middle. That actually could work, but implementing the arithmetic logic would get very ugly. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.