Mathematics Stack Exchange
Mathematics Stack Exchange

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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Boolean Simplification

I've been trying to simplify this equation: $Y = (¬AB + ¬C)(¬A + ¬D)$ .. into this equation. $Y = ¬A¬C + ¬C¬D + ¬AB$ Unfortunately I keep going in circles with expanding and minimizing the booleans. Any tips or advice? Thanks.
Sam
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How can this boolean algebra equation be solved?

(7EFEFEFF + A) ^ (A ^ FFFFFFFF) = 81010100 How can it be solved for the value A? where '+' means plus '^' is bitwise XOR EDIT: Forgot to mention. A is a hexadecimal variable
Jason
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Where did I go wrong with this Boolean simplification?

I am completely new to Boolean algebra, and I've tried to simplify this expression. All I did is tried to follow my lecturers methods, but I don't think it's right, and I have no idea how to do it. ¬a∧¬b∧¬c ∨ a∧¬b∧c ∨ a∧b∧¬c ∨ a∧b∧c First, I picked…
user111982
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My Boolean Expression Simplifications are correct or not?

1) I just want to know that my steps are correct or not? what are the missing steps. please help me. 2) Actually I can not simplify this is. So what are the missing steps at my trying path? please help me.....
user111554
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Boolean Expression Simplification

Dear all, I need help to simplify this Boolean algebra. Please give me a answer step by step. Thanks
user111554
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A detail in the proof of Stone representation Theorem

Let $(\mathcal{B},\sqcap,\sqcup,\leq)$ be a Boolean algebra. Let $x,y\in\mathcal{B}$. I want to prove the following implication: $$x\sqcap y'\leq 0\Rightarrow x\leq y$$ where $y'$ is the complement of $y$. I have checked that this works in the case…
Danae Kissinger
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how do you factor this boolean equation?

How do you factor this boolean equation $A'B'CD+AB'CD'+AB'C'D+ABCD$ I need help with where do I start from. What are the factors?
user103244
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Simplifying Sums of Product Expression obtained from 8-3 Priority Encoder (Computer Science)

I have an example for simplifying expressions in sums of product form, but I can't figure out which algebraic theorem was used to get rid of some of the variables: Step 1. (A'B'C'D'E'F'G) + (A'B'C'D'E) + (A'B'C) + (A) which simplifies to: Step 2.…
achabacha322
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How to simplify the following expression through Boolean algebra

Disclaimer: This was a homework problem from the first assignment of the semester - the assignment has long since been graded. For the life of me I can't crack this one - I don't understand what I'm not seeing here. I know from applying a Karnaugh…
Derek W
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Boolean Algebra - Demorgan Laws

I am given the problem: !((!A * B) * !((!B + C) * (!C * !D))) where ! = NOT, * = AND, and + = OR and I tried simplifying it using only Demorgan Laws (no absorption) and I got: (A + !B) + ((!B + C) + (C + D)) and I was just wondering if it was…
Josh M
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Simplifying Boolean Function

I am in a computer class with Karnaugh Maps and one of the questions is X 'Y Z + X 'Y 'Z + 'X Y 'Z + X Y Z and I need to simplify it where ' means not so 'x means not x. I think the answer is X 'Y + X Z + 'X Y 'Z but I am not sure, if I am wrong…
Tom
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boolean logic simplify

To prove: $(X+Y)(X'+Z) = XZ + X'Y$ I try to simply $(X+Y)(X'+Z)$ to $XZ + X'Y + YZ$ then I have no idea how to simply further. Thanks in advance!!
rMath
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How to find/generate a 6 variable Bent Function?

I want to find a Bent Function with 6 variables. I read some papers about how to generate Boolean Functions, but I don't want to implement an algorithm from zero just to find one function. It is also quite easy to test wether a function is Bent or…
erensezener
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Three Boolean Algebra Proofs - I just don't get it!

I'm having a very difficult time proving the following 3 expressions: $$\begin{align*} &x\cdot y\cdot z+x'\cdot z=y\cdot z+x'\cdot z\\ &x\cdot y+y\cdot z+x'\cdot z=x\cdot y+x'\cdot z\\ &(x'\cdot z'+x'\cdot y+x'\cdot z+x\cdot y)'=x\cdot…
echo
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Proving a boolean algebra question

Let $\sqsubseteq$ be a boolean ordering of the boolean algebra $X$, which means that for each $x$ and $y$ the following applies: $x \sqsubseteq y$ if $x \sqcap y = x$. Let $v, w, a, b \in X$ with $v \sqsubseteq a$ and $w \sqsubseteq b$. Show/prove…
user94450
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