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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Is this a valid Boolean expression?

a friend of mine asked me to look over some questions he was working on for practice, and I came across the question. Prove the following Boolean expression: $(X\lor(Y\leftrightarrow Z))\leftrightarrow((X \lor Y) \leftrightarrow (X \lor Z))$ I can't…
Detrimental
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Converting a Boolean expression to only use 3-input NAND-NAND

I need to convert some Boolean expression to only use 3-input NAND gates. Here is one example of an expression I'd like to convert: F = (A * C' * D)' + (A * B' * C * D') I would start by applying DeMorgan's law: F' = (A * C' * D) * (A * B' * C *…
Alex S.
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Express boolean function using NAND only?

How can I express $(\bar{x})y + \bar{z}$ using only NAND? I know the solution is $((x↑x)↑y)↑z$, but I don't understand how to get to there without expanding into an extremely long answer? The brute force technique given to me was: eliminate…
mathguy
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Can these sentences be used to define a Boolean Algebra?

T = {X ⊆ ℕ : X is finite} ∪ {X ⊆ ℕ : ℕ\X is finite} x∧y = x∩y x∨y = x∪y x' = ℕ\x Zero = ∅ One = ℕ I think it is correct but I am not sure if the finite (or infinite) set can make influence in defining Boolean Algebra.
FOREST
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How to transform this formula to DNF form?

I'm having troubles with converting this formula to DNF form: $[(p \vee q) \Rightarrow (q \vee r)] \Rightarrow [(p \Rightarrow q) \wedge \sim r]$ I've changed it to something like this (with steps): $\sim[(p \vee q) \Rightarrow (q \vee r)] \vee…
Miszka
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Simplification of majority function(boolean).

I have a boolean expression $$ABC+AB\bar C +A\bar B C+\bar A BC$$ This gives the majority boolean operator. That is it returns true when two or more of $A,B,C$ are true. I simplify it as $$AB+C(A\bar B+\bar AB)$$ I cannot show that it is equivalent…
Sonal_sqrt
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boolean simplification with k map

A'B'CD + A'BCD + ABCD + AB'CD + ABC'D' +ABC'D + ABCD' So I am trying to simplify this Boolean expression I need to use a K map but I also was trying to simplify it algebraically. This is what I got so far CD + ABC' + ABC'D So can this be…
Adil Ali
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Truth table of big boolean expression

A'B'C'D' + A'B'C'D + A'B'CD +A'BC'D'+A'BC'D + A'BCD + ABC'D' + ABC'D + ABCD I am trying to create the truth table for the expression above problem is that it will take a really long time to create it are there any short cut methods to get the out…
Adil Ali
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Novice error while simplifying boolean expression with XOR

I have the following expressions: $x = a⊕b , y = c⊕d, z = x⊕y $ So $x = ab'+a'b, y = cd'+c'd $ $z = xy'+x'y = (ab'+a'b) * (cd'+c'd)' + (ab'+a'b)'*(cd'+c'd)$ If I take the first term : $(ab'+a'b) * (cd'+c'd)' = (De Morgan) = (ab'+a'b) *…
XristosK
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How can you design a 3 bit adder using a 4 bit adder?

How can you design a 3 bit adder using a 4 bit adder? The description and/or the circuit's scheme would be great.
Iulia
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How to reduce A'B'+AB'+BC'D' to simplest form?

I wish to reduce the expression $A'B'+AB'+BC'D'$ to its simplest form. The notation for boolean variables $A,B,C,D$, for those who are not familiar, is : $+$ for logical OR operation $'$ for the logical NOT operation, and $AB$ means $A$ logical AND…
Zs11601
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Could anyone clarify why this Boolean expression AB'+AB'AC' = AB'?

Could anyone clarify why this Boolean expression AB'+AB'AC' = AB'? I did not understand what happened to the C'
Silvia De Olivera
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Simplification of boolean expression: $(A+BC’) (A(A+B’C)) + A’ + B’$

Good evening, As the title suggests, I need help to minimize a boolean expression and verify it with the $K$ map. I tried to solve it and the result is equal to $1$ but I can't get the same result with the $k$ map. I therefore believe that i made…
MikeK
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Problem of minimization and maximization

Minimize the expression: $F(a,b) = ab+ab'+a'b$. (A) $a'+b'$ (B) $a'+b$ (C) $a+b$ (D) $a+b'$ I have no idea how to solve this problem. Also how to maximize the expression and what is the value of maximization.
Baljeet
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A Boolean Algebra simplification problem

XY + (YZX)' + YZ So above I have this boolean expression I have done the work out and I got 1. I was wondering if that was the correct answer or did I miss a step.
Adil Ali
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