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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 .

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Number of ultrafilters in the free Boolean algebra on countably many generators

Let $A$ be the free Boolean algebra on denumerably many generators. How many ultrafilter does $A$ contain? How to prove it?
Beginner
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Boolean expression: how to find "don't care" numbers?

The boolean expression z+w' is received after simplification of the expression vw'y+v'wz+vyz+v'w'x'y'+v'w'xyz+vw'y'z'+vw'xy'z+v'w'yz' We don't know what are the don't care numbers, what are the numbers that are for sure don't care expressions? I…
BOB123
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2 bit adder implementation

wanted to know the minimum number of gates required to implement a $2$-bit adder, with $4$ inputs $(A_0, B_0, A_1, B_1)$, and $3$ outputs $(S_0,S_1, Carryout)$ using ONLY Universal gates Thank you.
Abdalrahman Abouzaied
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4-bit's 2's Complement using minimum number of Universal gates only?

I'm trying to design a $4-$ bit's $2$' complement using minimum number of universal gates ONLY (NAND,NOR, NEGATIVE OR, NEGATIVE AND) , hence, minimum number of ICs.I got $4$ simplified output expressions ($w,x,y,z$) from the Truth table and k - map,…
Abdalrahman Abouzaied
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Solving (A ror 5) xor A = X

I am trying to solve following formula: $(A\ \mathrm{ror}\ 5)\ \mathrm{xor}\ A = X$ where $X$ is an unsigned 32-bit integer which is known, and $A$ is an unsigned 32-bit integer which needs to be calculated. $\mathrm{ror}$ is rotate right through…
Daniel Marschall
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Simplify (using the laws of Boolean algebra)

I have: $(\overline{A} \land \overline{B} \land \overline{C}) \lor (\overline{A} \land \overline{B} \land C) \lor (\overline{A} \land B \land C) \lor (A \land \overline{B} \land \overline{C}) \lor (A \land B \land \overline{C}) \lor (A \land B \land…
Wind
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An exercise of Boolean algebras

On page 87, Introduction to Boolean Algebras,Steven Givant,Paul Halmos(2000) Give an example of a subalgebra $B$ of a Boolean algebra $A$ and of a subset $E$ of $B$ such that $E$ has a supremum in $B$ but not in $A$. The example that occured to…
Metta World Peace
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Vector of boolean values of $F(n)$

A boolean function $F=F(x_{1},x_{2},x_{3},x_{4})$ has the vector of its values $w(F)=1010101000111111$ (the leftmost $1$ is $F(0,0,0,0)$ and so on). I need to find the vector of values for $F_1=F(x_{4},x_{3},x_{2},x_{1})$. Problem: of course, I can…
alekscooper
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Why is the distributive law, $A+BC=(A+B)(A+C)$ not true in real algebra?

It's only true in boolean algebra. But why is that? At what point does that break? What is special about real algebra that breaks that rule?
sigsegv
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What is a function from a domain to predicate functions called

Say, I have finite tuple $x$: $ x \in X \times X' \times X'' \times \ldots $ Now I define a $Y$, a set of predicate functions over this tuple: $\forall y \in Y. y: X \times X' \times X'' \times \ldots \to \mathbb{B}$ But I want to have a special…
hgiesel
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Simplifying Boolean expression.

I have to show that the following expression are equal using the simplification rules: $$x' y z + x y' z + x y z' + x' y z' + x y' z' + x' y' z = x y' + y z' + z x'$$ But I can only get to: $$y'z + y'x + x' y z$$ Please let me know what I am doing…
johnny layman
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If $B$ if a finite Boolean algebra, then it contains an atom

Let $B=\{a_1,\dots,a_n,0,1\}$ be a finite Boolean algebra. I want to show that there exists an atom $x\in B$. So I want to show that there exists $x\in B$, such that for each $a\in B$ for which $a
Sha Vuklia
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Example of a 4+ boolean algebra

I just read about how Boolean Algebras can have more than 2 elements (0, 1). And this shines some more light: All finite boolean algebras have an even number of elements? I am wondering though how this is possible, or what it looks like. I always…
Lance
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Boolean algebra with 5 sets

Simplify the following Boolean expression. Your final equation should be in minimized sum-of-products form. W = B' (A + BC + B'CD + A'D) So far I have: Use distributing: AB' + B'BC + B'B'CD + A'B'D Complementary: AB' + 0 + B'B'CD + A'B'D Is this…
user9419099
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How can Quine McCluskey be applied for product of sum

I know the algorithm of QM for SoP but I'm not sure whether for PoS I should group them by 0's or group them by 1 and in the end simply use products instead of sum.Searched for this but can't find it
Lola
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