SUM (Ternary Gate)

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

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	-
+	+	+