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