Notes on Ternary Logic.
Along with ternary arithmetic, a computer built of ternary hardware can also exploit ternary logic.
Consider the task of comparing two numbers. In a machine based on binary logic,
comparison is often a twostage process. First you ask, "Is x less than y?";
depending on the answer, you may then have to ask a second question, such as
"Is x equal to y?" Ternary logic simplifies the process: A single comparison
can yield any of three possible outcomes: "less," "equal" and "greater."
Single Input Gates
The gate names uses the heptavintimal notation.
Reversible Gates
 Identity(U): The most dull gate (number 8) this does not change the
input. It is its own complement. Applying it any number of times get you back
to your intial value.
 Negation(E): Balanced ternary gates have a tighter relationship
between logical and mathmatical negation. The are the same bitwise operator. It
is its own complement. Applying it multiple time every even application brings
back the intial value.
 Increment(G) and Decrement(K): These gates can arithmetically
be thought of as single trit increment or decrement without carry, but with
roll over. These gates are also complementary . Every 3 applications of either
one of these gates in a row bring back the intial value.
 And gates O and S.
To learn more, see reversible computing.
 +  0    Number  Name  Definitions 
0        13  False  NEG(LAX(LAX)) 
A      0  12   NEG(LAX) 
B      +  11  Decoder()  DEC(DEC(LAX)) 
C    0    10  Abn  NEG(LAX(DEC)) 
D    0  0  9   DEC(LAX(NEG)) 
E    0  +  8  Negation  NEG 
F    +    7  Decoder(0)  DEC(DEC(LAX(DEC))) 
G    +  0  6  Increment  DEC(DEC) 
H    +  +  5   DEC(NEG(LAX(NEG))) 
I  0      4   NEG(LAX(NEG)) 
J  0    0  3   DEC(LAX(DEC)) 
K  0    +  2  Decrement  DEC 
L  0  0    1   DEC(LAX) 
M  0  0  0  0  Clear  DEC(LAX(LAX)) 
N  0  0  +  1   NEG(DEC(LAX)) 
O  0  +    2   NEG(DEC) 
P  0  +  0  3   NEG(DEC(LAX(DEC))) 
Q  0  +  +  4   LAX(NEG) 
R  +      5  Floor/Decoder(+)  DEC(DEC(LAX(NEG))) 
S  +    0  6   DEC(NEG) 
T  +    +  7   DEC(NEG(LAX(DEC))) 
U  +  0    8  Identity  NEG(NEG) 
V  +  0  0  9  Flat  NEG(DEC(LAX(NEG))) 
W  +  0  +  10  Abs  LAX(DEC) 
X  +  +    11  Ceil  DEC(NEG(LAX)) 
Y  +  +  0  12  Lax  LAX 
Z  +  +  +  13  True  LAX(LAX) 
AND 
B 
F 
U 
T 
A 
F 
F 
F 
F 
U 
F 
U 
U 
T 
F 
U 
T 
OR 
B 
F 
U 
T 
A 
F 
F 
U 
T 
U 
U 
U 
T 
T 
T 
T 
T 
Inputs 

Outputs 
X 
Y 

TNAND 
TNOR 
−1 
−1 

1 
1 
−1 
0 

1 
0 
−1 
1 

1 
−1 
0 
−1 

1 
0 
0 
0 

0 
0 
0 
1 

0 
−1 
1 
−1 

1 
−1 
1 
0 

0 
−1 
1 
1 

−1 
−1 