Balanced Ternary: Difference between revisions

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{| class="wikitable" style="text-align: left;"
{| class="wikitable" style="text-align: left;"
! A || B || Xor
! A || B || Xor
|- -1 | -1 | -1
|-
|- -1 | 0 | 0
| - || - || -
|- -1 | 1 | 1
|-
|- 0 | -1 | 0
| - || 0 || 0
|- 0 | 0 | 0
|-
|- 0 | 1 | 1
| - || + || +
|- 1 | -1 | 1
|-
|- 1 | 0 | 1
| 0 || - || 0
|- 1 | 1 | 1
|-
| 0 || 0 || 0
|-
| 0 || + || 0
|-
| + || - || +
|-
| + || 0 || 0
|-
| + || + || -
|}
 
=== Add and Carry===
{| class="wikitable" style="text-align: left;"
! A || B || Add || Carry
|-
| - || - || 0 || -
|-
| - || 0 || - || 0
|-
| - || + || 0 || 0
|-
| 0 || - || - || 0
|-
| 0 || 0 || 0 || 0
|-
| 0 || + || + || 0
|-
| + || - || 0 || 0
|-
| + || 0 || + || +
|-
| + || + || 0 || +
|}
|}

Latest revision as of 16:59, 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 + 0
+ - +
+ 0 0
+ + -

Add and Carry

A B Add Carry
- - 0 -
- 0 - 0
- + 0 0
0 - - 0
0 0 0 0
0 + + 0
+ - 0 0
+ 0 + +
+ + 0 +
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