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. Another gate is needed to perform ternary addition.
While there is a [[XOR (Ternary Gate)|Ternary XOR]] gate, it's usefulness does not fit 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.


It is also useful for cryptography being balanced, self-negating, associative, and commutative.
It is also useful for cryptography and error correction being balanced, self-negating, associative, and commutative.


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Revision as of 01:23, 11 June 2024

Modulo-3 Sum

Uses

While there is a Ternary XOR gate, it's usefulness does not fit with what the Binary XOR can do. Another gate is needed to perform ternary addition.

SUM does mod 3 addition, returning the remainder.

It is also useful for cryptography and error correction being balanced, 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

SUM B
- 0 +
A - + - 0
0 - 0 +
+ 0 + -
A B Y
- - +
- 0 -
- + 0
0 - -
0 0 0
0 + +
+ - 0
+ 0 +
+ + -

NSUM

NSUM B
- 0 +
A - - + 0
0 + 0 -
+ 0 - +
A B Y
- - -
- 0 +
- + 0
0 - +
0 0 0
0 + -
+ - 0
+ 0 -
+ + +