Boolean algebra manipulates two-state binary values

[ouverson]

I'm reading the 2nd edition.

1.1 Boolean Algebra

"Boolean algebra manipulates two-state binary values that are typically labeled true/false, 1/0, yes/no, on/off, and so forth."

Are there more or less than two states of binary values?

[WBahn]

The word "binary" means exactly two.

A binary start system as exactly two stars.

A binary logic system has exactly two possible states.

You can have logic systems with more than two states, but it is not binary logic. If it has three states then it is a trinary logic system. In general, logic systems with more than two states are referred to as multi-valued logic systems.

Less than two states is meaningless. If you only have one state, then you have no ability to describe any variation at all. Even less meaningful would be zero states because then not only can you not describe any changes in a variable, you can't even describe a variable at all.

[ouverson]

Thank you for sharing about "trinary logic systems" and "binary stars".

Since binary values can only have 2 states, why use the phrase "two-state binary values"? Isn't that redundant?

[WBahn]

I agree it's redundant. My guess is that they figure that the meaning of "binary" might be new to some readers and so they wanted to make it clear that they were talking about a system with exactly two possible states, but also wanted to use the common "binary" terminolody. I think it could have been worded better. Perhaps, something like, "in a two-state system, also known as a binary system, the states are often represented by...."

[ouverson]

I agree. Thank you.