SUM (Ternary Gate): Difference between revisions
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== Uses == | == Uses == | ||
While there is a [[XOR Ternary Gate|ternary XOR]] gate, it's usefulness does not align with what the [[XOR Binary Gate|binary XOR]] can do. | While there is a [[XOR Ternary Gate|ternary XOR]] gate, it's usefulness does not align with what the [[XOR Binary Gate|binary XOR]] can do. Another gate is needed to perform ternary addition. | ||
SUM does mod 3 addition, returning the remainder. A Half and Full Adder use SUM in place of an XOR. | SUM does mod 3 addition, returning the remainder. A Half and Full Adder use SUM in place of an XOR. |
Revision as of 04:46, 29 May 2024
Modulo-3 Sum
Uses
While there is a ternary XOR gate, it's usefulness does not align with what the binary XOR can do. Another gate is needed to perform ternary addition.
SUM does mod 3 addition, returning the remainder. A Half and Full Adder use SUM in place of an XOR.
It is also useful for cryptography being symmetrical, self-negating, associative, and commutative.
A ⊕ B = C
C ⊕ A = B
A ⊕ C = B
B ⊕ C = A
A ⊕ 0 = A
0 ⊕ A = A
Truth Tables
SUM | B | |||
- | 0 | + | ||
A | - | + | - | 0 |
0 | - | 0 | + | |
+ | 0 | + | - |
A | B | Y |
- | - | + |
- | 0 | - |
- | + | 0 |
0 | - | - |
0 | 0 | 0 |
0 | + | + |
+ | - | 0 |
+ | 0 | + |
+ | + | - |