Building a hardware ternary computer. Help wanted!

I will build a ternary computer, where a positive current is considered 1 and a negative current is considered -1. But I can't manage both 1

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Description

I’m planning to build a ternary computer where a +- wiring sequence is assigned a value of 1 and a -+ wiring sequence is assigned a value of -1.

Theoretically, I plan to treat AND as:

1 + 1 = 1
-1 + -1 = -1
everything else = 0

and NOT as:

1 + 1 = -1
-1 + -1 = 1
1 + 0 = 1
-1 + 0 = -1
everything else = 0

I intended to connect AND on the left and NOT on the right to reproduce one-digit + one-digit operations, but I simply cannot reconcile the fact that 1 + 1 = 1 and 1 + 0 = 1 at the same time.

If you could lend me a hand, I would appreciate it.
※The goal is to build an operating system