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Questions tagged [boolean-algebra]

Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Use this tag for questions about Boolean algebras as structures, or about functions defined from/to Boolean algebras. For Boolean logic use the tag propositional-calculus.

Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Use this tag for questions about Boolean algebras as structures, or about functions defined from/to Boolean algebras.

A Boolean algebra uses Boolean variables, typically denoted by capital letters, e.g. $A,B$, which can only take the values $0$ or $1$. Operators are $\land$ (conjunction), $\lor$ (disjunction) and $\lnot$ (negation).

For Boolean logic use the tag .

3083 questions
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What is the meaning of this sentence?

Please see the below sentence: Namely, $A$ and $B$ are equivalent iff setting any variable $x$ to $false$ resp. $true$ yields two respectively equivalent DNF/CNF pairs. What is the meaning of "$false$ resp. $true$"?
user4704857
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Are there functions of boolean parameters that must evaluate more than two variables?

My question is more from a digital logic background, and what is possible on computers, though I am curious what the answer is for real numbers. Consider a function that performs a bitwise AND on two inputs, perhaps implemented as logic gates in…
Burnsba
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Why choosing 1 or 0 for the dont care values give different function in a Karnaugh Map?

If I have a Karnaugh Map with dont care values . I can give any dont care the value 1 or 0 depend on my needs. But why if I will choose 1 for the dont care values, it will give me a function $f$ And if I will choose 0 instead, the function I will…
idan di
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Karnaugh map grouping of element

In Karnaugh map ($4\times 4$) can we group an element that is shared two three different groups. I think answer should be no but I do not know why it is?Can anybody provide a reason in support of this answer.
tyt
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Boolean Algebra simplifcation

I have an expression I need to simplify for a class assignment, yet I simply can not figure out how to apply the rules in this case. Can someone put me on the right direction? w’x’y’z + w’xy’z + wxy’z + wx’y’z + w’x’yz
needhelp
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Clarity on Boolean Algebra and Rings

I'm trying to wrap my head around Abstract Algebra, Boolean rings, and it's a little difficult. So I understand the ring (I believe it's a ring) <ℤ ,x, +, -, 0, 1 > is normal integer arithmetic stuff. We can add and multiply in it and still be in ℤ…
Kyobreck
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Stuck in Boolean Algebra equation

I have this equation in Boolean Algebra: $x*y*z+x'*y*z+x*y'*z+x*y*z' = y*z+x*z+x*y$ I got this: $= yz(x+x')+xy'z+xyz'$ $= yz+xy'z+xyz'$ And from here I tried multiple things but it goes wrong like: $yz+x(y'z+yz')$ $yz + x$ Since y'*y and z'*z =0…
Sinan Samet
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Boolean Expression Simplifying explanation

Currently have worked xz' + x'y + (yz)' Down to z' + x'y + y' Is this its simplest form? METHOD: xz' + x'y + (yz)' -> De-Morgan on (yz)' xz' + x'y + y' + z' -> Commutative xz' + z' + x'y + y' -> Simplifying xz'+ z' z'(x + 1) + x'y + y' ->…
MichaelMariani
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Help with Simplifying boolean algebra, not sure if i have done it correctly.

I have no idea how to do boolean algebra, First question is x'y + x(x + y') I need to first draw a circuit diagram(logic gate) and then simplify it and draw a simplified logic gate. As of now I only have it down to x'y + xx + xy' Am I right in…
MichaelMariani
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Confirmation of an answer of a question on Boolean Algebra

Here are the solution I have worked out. Is it correct? Given $C + BC'$: $C + B' + C'$ $C + (B'+C')'$ $C + B + C$ $C (C + B + C)$. Is the answer (2)?
firstimer08302
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canonical expression in compact form??

Does canonical expression in compact form need to have all the variables in it? For example, if I have a,b,c, and d variables and the compact form comes out to be just c+d, is this possible? For example: If I have an expression…
Ananymus
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quick question about writing consensus theorem

In order to prove $bc + abc + bcd + a'(d+c) = abc + a'c + a'd$ I got it down to $abc + a'c + a'd + bc + bcd$ (LHS), and from there I factor out $bc$ from $bc + bcd$, which is $bc(1+d)$, simplifies into $bc$, what should I do after?
Ananymus
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Boolean Logic using proofs

ABC' + C = AB + C I understand this using venn diagrams and intuition. However, I am not able to derive the proof for getting from one side to the other. It's probably very simple step that I keep missing. Please enlighten me.
Jonathan
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Quick question on Bitwise operations

I have some questions for homework to do with Bitwise operations, now it's a simple task but it doesn't actually explain how to handle the questions which is why I'm asking here before I begin attempting the lot of them (10 similar questions) First…
Ice Art
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How can I show a set B with 8 elements and two operations, such that the axioms of huntington for boolean algebra holds?

If It was about two members I would have choose B={0,1} with the operations: AND , OR And prove this. But how can I do this with 8 elements?
idan di
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