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 .

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Larger circuit design for same boolean function?

I've designed this circuit with 4 logic gates, and did Karnaugh map's simplification and Quine McCluskey method. However I found out that actually my circuit design is already optimized and I can't really compare how the simplifications offer a less…
diegoaguilar
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Simplification of sum of products

I have the following equation: A'BC + AB'C + ABC' + ABC I know I can simplify one part of the equation factoring AB(C' + C) = AB I looked at the results in an online solver and the simplification of the whole function is BC + AC + AB However I don't…
FERN4V3
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Distinct Karnaugh Maps grouping?

I got a table truth with some minterns which I mapped to a Karnaugh Map, then I can see an obvious choice for grouping. But I'm wondering wether in this case is possible to do any other different to the first one?
diegoaguilar
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Can a CNF formula contain no clause or contain empty clause?

The definition of CNF formula that i found at internet is that CNF formula is a conjunction of clause, and clause is a disjunction of literal. But i haven't found anywhere the answer of whether a CNF formula can not contain any clause and whether…
LLL
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Tautology problem

Show that $((p \vee q) \wedge \neg (\neg p \wedge (\neg q \vee \neg r))) \vee ( \neg p \wedge \neg q) \vee (\neg p \vee r )$ is a tautology (without using truth table). After simplification I got $ ((p \vee q) \wedge (p \vee r)) \vee \neg (p \vee q)…
Lila Sharma
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Simplifying a short Boolean expression

\begin{align*} A’B + A’B’C + ABC’C’ + AB’ + AB’C’ &= A’B + A’B’C + ABC’ + AB’ + AB’C’ \\ &= A’(B +B’C) + ABC’ + AB’(C’+1) \\ &= ??? \end{align*} I'm stuck after this. Please help me!!
David
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Line follower robot using max 8 NAND gates

So I have to figure out the logic for a line follower robot using at maximum 8 NAND gates (2 7400HC series NAND circuits). The robot has 3 sensors, which give 1 on a black surface and 0 on a white surface. The robot has 2 motors, one on the left and…
TasH
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Sum of products boolean algebra with 3 inputs

I have the following expression A'.B.C + B'.A.C + C'.B.C + C'.A'.B' I've tried taking out some variables and applying demorgan laws and it didnt, I also tried XOR but it would result in C.A.B instead, any suggestions or is completely simplified, I…
Programmer
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Can you write the shortest boolean formula for this truth table?

I am looking the the shorted formula possible, can you help to simplyfy it? ((not A and B and C and not D) or (not A and B and C and D) or (A and not B and C and not D) or (A and not B and not C and D)) possibly with explaination of each step y is…
giacomo venturelli
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Implement F=ab+a'c+b'c' using AND/OR and no NOT

Implement F=ab+a'c+b'c' using only AND/OR gates. And we do not have any inverterad signals to use (guess that means we have to make the inverterad signals from our AND/OR gates. But I'm just stuck. Should I try using K-map, because that just gives…
Gripen
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Reduce to sum of products

I'm given the equation $F = (x+w)z' + x(y+z) + xz$ The inverse I got is $F' = [(x'+z)*(w'+z)]*[(x'+y')*(x'+z')]*[x'+z']$ To start I would expand $F'= [x'w' + x'z + zw'+zz] * [x'x' + x'z' + y'x' + y'z'] * [x'+z']$ What laws can I apply here to…
user1766888
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What law results from this? Boolean algebra

Hi guys can you help me with the following task: Using the laws of Boolean algebra, show the validity of the following expression: $ (x \land y) \lor (x \land \overline y) = x $ I have done: $ (x \land y) \lor (x \land \overline y) = x \land…
alex1888
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Simplification of boolean functions

I have the following problem: Simplify the following Boolean functions by algebraic transformation. Express the result in disjunctive normal form (DNF). i) $j(a, b, c, d)=a \bar{b}+c+\bar{a} \bar{c} d+b \bar{c} d$ ii) $k(a, b, c,…
Rico1990
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How do I simplify this Boolean expression

Number 5 in the following image is what I need help with. So I had a test a few days ago and I couldn’t simplify this Boolean expression. The answer as shown in the image is supposed to be ~a~bc~d. Does anyone mind sharing a solution? ! my attempt
leun
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$(xy'+xy)+xz'$ (simplify to $X$ using boolean algebra)

$$(xy'+xy)+xz'$$ Using boolean algebra I achieve $x + xz'$, which is pretty obvious by just looking at the problem, however I can't find another way to go after there in order to cancel the $z',$ since there is no $xz$ or similar term to cancel the…
Miguel Rodriguez
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