What do you guys think of the number system with base -2? I came across this idea when I did my master thesis and implemented some multiplier circuits for it. It is called nega-binary. The (only?) cool thing about it is that there is no special position in the vector of bits that is defined differently from the other positions to be able to encode negative numbers; it is inherently part of the number system. The weights of the bits from right to left are 1, -2, 4, -8, 16, -32, and so forth. To give some examples:

-6: 01110 -5: 01111 -4: 01100 -3: 01101 -2: 00010 -1: 00011 0: 00000 1: 00001 2: 00110 3: 00111 4: 00100 5: 00101 6: 11010