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I'm trying to convey to some folks some logical and bitwise operators such as AND, OR, XOR, &c in programming languages such as C &| Java. Though these I guess could be considered "boolean" operators there is no "Boolean Algebra" in here, just the results of various operation, yes?

I've never heard of Boolean Arithmetic, but would one consider these simple questions

5 AND 8 = ?

boolean arithmetic (operating bitwise) or rather logical or bitwise arithmetic?

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What is algebra (or arithmetic) other than the results of various operations? – Qiaochu Yuan Sep 28 '10 at 14:01
up vote 6 down vote accepted

But there is boolean algebra here. Namely, you can consider an $\rm n$-bit integer as a characteristic function for a subset of $\rm\: n = \{0,1,\ldots,n-1\}$, viz. bit $\rm i$ of $\rm k$ is $1$ iff $\rm i$ lies in the subset represented by $\rm k$. The bitwise boolean operations suffice to define all of the boolean algebra operations in this powerset boolean algebra.

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The whole explanation went above my head, can you please explain it in some detail. For example recently I was trying to solve $$1010 \text{ OR } 0011$$ though I can solve it bitwise but is there any other insight to be gained from it? – vivek Apr 14 at 16:09

The terms boolean, binary, and bitwise arithmetic are all equivalent in my mind. However, it is most commonly referred to as binary arithmetic in my experience.

Boolean algebra however is a more general field (encompassing more than just arithmetic), and is really synonymous for classical propositional calculus.

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