Order of operations in boolean algebra

AI Thread Summary
The order of operations in Boolean algebra is NOT, AND, and then OR, with expressions in brackets evaluated first. XOR is treated differently in programming languages, where it can have precedence over AND and OR but is lower than bitwise AND. The discussion emphasizes that while understanding precedence is important, using parentheses can eliminate any ambiguity in expressions. The consensus is that clarity in expression is key, regardless of the order of operations. Ultimately, using parentheses is the best practice to ensure correct evaluations.
Bipolarity
Messages
773
Reaction score
2
I have a rather technical question in boolean algebra to which I was not able to find an answer.

What is the order of operations in boolean algebra?
Is it first logical NOT, logical AND, logical OR, and finally logical XOR?

Correct me if I am wrong.

BiP
 
Physics news on Phys.org
The order of Boolean operations from high to low priority is NOT, AND, OR, while expressions inside brackets are always evaluated first.

http://www.doc.ic.ac.uk/~dfg/hardware/hardware.html, Handout, page 2.
 
What about XOR?

BiP
 
Since xor is equivalent as not equals, at least in C-based languages xor (as !=) has precedence over logical and (&&) and logical or (||). However, bitwise and (&) has precedence over bitwise xor (^), which in turn has precedence over bitwise or (|).

In the end, does it really matter? Just use parentheses and there's no doubt.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
Back
Top