Balanced Ternary: Difference between revisions
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| Line 17: | Line 17: | ||
! A || B || Xor | ! A || B || Xor | ||
|- | |- | ||
| - | | - || - || - | ||
|- | |- | ||
| - | | - || 0 || 0 | ||
|- | |- | ||
| - | | - || + || + | ||
|- | |- | ||
| | | 0 || - || 0 | ||
|- | |- | ||
| | | 0 || 0 || 0 | ||
|- | |- | ||
| 0 || 1 || | | 0 || 1 || 0 | ||
|- | |- | ||
| 1 || -1 || 1 | | 1 || -1 || 1 | ||
| Line 34: | Line 34: | ||
|- | |- | ||
| 1 || 1 || -1 | | 1 || 1 || -1 | ||
|} | |||
=== Add and Carry=== | |||
{| class="wikitable" style="text-align: left;" | |||
! A || B || Xor || Carry | |||
|- | |||
| -1 || -1 || -1 || -1 | |||
|- | |||
| -1 || 0 || 0 || -1 | |||
|- | |||
| -1 || 1 || 1 || -1 | |||
|- | |||
| 0 || -1 || 0 || -1 | |||
|- | |||
| 0 || 0 || 0 || -1 | |||
|- | |||
| 0 || 1 || 0 || -1 | |||
|- | |||
| 1 || -1 || 1 || -1 | |||
|- | |||
| 1 || 0 || 0 || -1 | |||
|- | |||
| 1 || 1 || -1 || -1 | |||
|} | |} | ||
Revision as of 14:44, 18 June 2019
Logic
While logical "true" and "false" are all that is computationally required, in real time systems and "unknown" state is meaningful. And this maps well allowing -true == false, -false == true and -unknown == unknown.
Potentially this could allow for un-clocked logic.
Negative Symmetry
Twos compliment has the useful property that -0 == 0, but this has the undesireable symmetry that -MaxNegative == MaxNegative.
Data vs Electrical Complexity
The data density of a base 3 is 58% higher than base 2, but the complexity should not increase that drastically.
Gates
Base 2 has 16 total gates, 12 "meaningful" gates. Base 3 has 19683 gates, 19679 meaningful gates
XOR
| A | B | Xor |
|---|---|---|
| - | - | - |
| - | 0 | 0 |
| - | + | + |
| 0 | - | 0 |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | -1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | -1 |
Add and Carry
| A | B | Xor | Carry |
|---|---|---|---|
| -1 | -1 | -1 | -1 |
| -1 | 0 | 0 | -1 |
| -1 | 1 | 1 | -1 |
| 0 | -1 | 0 | -1 |
| 0 | 0 | 0 | -1 |
| 0 | 1 | 0 | -1 |
| 1 | -1 | 1 | -1 |
| 1 | 0 | 0 | -1 |
| 1 | 1 | -1 | -1 |