Why Do Computers Use Binary Logic Instead of Ternary?

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Computers use binary logic because it simplifies design and implementation, relying on two distinct states (0 and 1) that facilitate reliable switching. Early computing systems favored binary due to its straightforwardness, making it easier to develop programming schemes that are efficient and effective. Introducing ternary or multi-valued logic would complicate processing speed and system architecture without significant advantages in most applications. While tri-state logic could represent more values, the complexity it introduces often outweighs its benefits. Overall, binary remains the simplest and most practical choice for computing systems.
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Why computer use binary logic (0,1) instead of use a ternary or something else?
 
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In the early computing systems it was easier to use two hard states 0 and 1 rather than three or more discrete levels as it means that you can hard switch your devices. Once your programming schemes are based around binary and working well, why change to another system.
What would be the advantage of using a tri-state logic in the majority of applications? This needs to be considered both from speed of processing and ease of implimentation.
 
it is not just easier to use, it is simplest possible logic (you can't really make a logic out of one value), but it is quite enough for everything, at the same time. suppose you have some 4-valued predicate F(x) that can be all the values v1, v2, v3 or v4. In terms of 2-valued predicates, that translates into two predicates P(x) and Q(x), that are defined like this:
  • P(x) = v1 iff F(x) = v1, or v2;
  • Q(x) = v1 iff F(x) = v1, or v3
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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