It simplifies many arithmetic operations, particularly addition and comparison. Why Use Base 3? (Radix Economy)
In our everyday system, we use ten digits: 0 through 9. In binary (Base 2) , we use two: 0 and 1. In ternary (Base 3) , we use three digits: 0, 1, and 2 .
: Show how numbers are built differently when each position represents a power of 3 instead of 2 or 10. Retrospective on making Base 3 | Menial
| Decimal | Base 3 | Why? | |---------|--------|------| | 0 | 0 | | | 1 | 1 | | | 2 | 2 | | | 3 | 10 | (1 \times 3 + 0) | | 4 | 11 | (3 + 1) | | 5 | 12 | (3 + 2) | | 6 | 20 | (2 \times 3 + 0) | | 7 | 21 | (6 + 1) | | 8 | 22 | (6 + 2) | | 9 | 100 | (1 \times 9 + 0 + 0) | | 10 | 101 | (9 + 1) | | 11 | 102 | (9 + 2) | | 12 | 110 | (9 + 3) | | … | … | |
Example: ( 1T1_\textbal ) (where T = -1) means: [ 1 \times 9 + (-1) \times 3 + 1 = 9 - 3 + 1 = 7 ]