Here's something I discovered (stumbled upon) on about 22nd December 2002.
I haven't tried seeing whether you can use other negative-integer bases yet.
I doubt that base -2 is much use to anyone, but one interesting property
is that you never seem to need a minus sign. You can represent positive and
negative numbers without needing a plus or minus sign.

I'm not sure whether there are any easy-to-use rules for arithmetic in this
base. Some numbers seem cumbersome to represent in base -2. Just look at
-0.75 and -0.875: They use TWO digits to the left of the point to the right
of (-2)^0.


Base -2 :

-32 16 -8 4 -2 1 -0.5 0.25 -0.125 

0.125 = 0.011
0.25  = 0.010
0.375 = 1.101
0.5   = 1.100
0.625 = 1.111
0.75  = 1.110
0.875 = 1.001

-0.125 = 0.001
-0.25  = 0.110
-0.375 = 0.111
-0.5   = 0.100
-0.625 = 0.101
-0.75  =11.010 // WTF?!
-0.875 =11.011 //

-16=110000
-15=110001
-14=110110
-13=110111
-12=110100
-11=110101 
-10=001010
-9 =001011
-8 =001000
-7 =001001
-6 =001110
-5 =001111
-4 =001100
-3 =001101
-2 =000010
-1 =000011
0  =000000
1  =000001
2  =000110
3  =000111
4  =000100
5  =000101
6  =011010
7  =011011
8  =011000
9  =011001
10 =011110
11 =011111
12 =011100
13 =011101
14 =010010
15 =010011
16 =010000