Balanced Ternary System
First lets build the basic ternary (base 3)
number system. The symbols are 0, 1, 2 and the columns are based on powers of
3. (1,3,9,27…)
base 10 
base 3 

0 
0 

1 
1 

2 
2 

3 
10 
one 3 no units 
4 
11 
one 3 one 1 
5 
12 
one 3 two 1's 
6 
20 
two 3's no 1's 
7 
21 

8 
22 
two 3's two 1's 
9 
100 
one 9 
10 
1001 
one 9 one 1 
The balanced ternary system uses the symbols , 0, 1 where the implies subtracting the
value. You could substitute a 1 for every . Here is the same table as above represented in
balanced ternary.
base 10 
base 3 

0 
0 

1 
1 

2 
1 
one 3 minus 1 
3 
10 
one 3 no units 
4 
11 
one 3 one 1 
5 
1 
one 9 minus one 3 minus 1 
6 
10 
one 9 minus one 3 
7 
11 
one 9 minus 3 plus one 1 
8 
10 
one 9 minus one 1 
9 
100 
one 9 
10 
101 
one 9 one 1 