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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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Boolean SOP Expression Simplification: $F(a,b,c,d) = (a+d)(a'b+c'd)(ac+bd)'$

my answer that I have gotten is $b'c'd + a' b d'$ however, the answer given to me was b'c'd can someone tell me whether I am correct
kero
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Simplify 4-term Boolean Algebra expression

How do I get from this: $F = AB' + AC' + AD + C'D'$ to this: $F = AB' + AD + C'D'$ Not sure how the $AC'$ disappeared.
Or Svantovit
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How to read Hasse diagrams and how they can describe a Boolean Algebra?

Consider a Hasse Diagram for a Boolean Algebra of Order 3 Just by using the diagram and defined Boolean Algebra System as : $\langle B, \vee ,\ \cdot \ , \bar{\ \ } \ ,0, 1 \rangle$ and for any 3 of its arbitrary elements $a, b, c$ in $B$ the…
amarVashishth
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Sum of Products Expression using $K$-map

Determine the minimum SOP, sum of products expression using $K$-Map $F(A,B,C,D,E) = (A’ + B + C’ + D + E’)(A’ + C’ + D + E )(A’ + C’ + E )AC’$ My problem is, in my class room we have always done this from the POS form or SOP form, but this is not…
Tanner Summers
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Is canonical SOP/POS form for a boolean expression unique?

I was trying to find equivalence between two boolean expressions and thought if I convert both of them to canonical sum of product or product of sum form they should match. But I am not sure if these forms are unique for a boolean expression, are…
Samik
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Convert a'+b(a+b')(b+c') to sum of products and product of sums using boolean algebra.

Sum of products F = a'+b(a+b')(b+c') = a'+ ab + bb' (b+c') = a'+ab So that's about as far as I've gotten. I'm trying to find a step by step guide on how to do these sorts of problems but still unclear as to how. Any sort of directions would be…
borderlineNovice
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Sigma notation with minterms

I'm trying to understand what is meant by the notation $F(x,y,z)=\sum m(0,1,2,3)$ I found this webpage but it's still unclear to me. It states the function F is defined by the truth table $A$ $B$ $C$ $F$ 0 0 0 0 0 0 1 1 0 1 0 …
Celeritas
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Reducing boolean algebra

So I got this equation: (NOT A + B) x ( A + C) When I try to reduce this I get (Not A AND C) OR (A AND B) OR (B AND C) But wolframalpha.com(here) says it ends up being A'C + AB. I also tried to input my original reduction and got this (here) whitch…
Sumsar1812
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sum of products Boolean algebra simplification

I have a question that states the following: Use algebraic manipulation to show that for three input variables x1 , x2 , and x3 ∑(1,2,3,4,5,6,7) = x1 + x2 + x3 I'm assuming it wants the minimum sum of products to prove its equality to x1 + x2 + x3…
cellsheet
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A question in boolean calculus

I've looked everywhere on the web, in my note and to fellow student without any of them able to explain to me. Here is my question to you. I can't figure out how to calculate this boolean expression Can you help me solve : ¬(¬x+x¬y) (sorry i…
Chax
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Simple Boolean Algebra Exercise but stuck

I have the following exercise that I can't really solve or I am not happy with the result: If Team A loses, Team B and C will lose too If the Teams A and B win, Team C will lose If Team B wins, Team A will win too and Team C will lose If the Teams…
MathiveProblem
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Boolean equation - bitwise AND operator

I have equation: (x AND B) XOR x = C where x - is unknown variable, B and C are constant. I need just one solution x that will satisfy this equation. How I can do this?
rnd
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Simplifying a Boolean function from a Kernaugh Map

Given the three variable Karnaugh Map: x\yz 00 01 11 10 \___________________ 0 | 0 1 1 0 1 | 1 0 0 1 I am supposed to write a simplified expression for the Boolean function. Based on this KMap, I figured there should be…
Badger
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Boolean Algebra fundementals

A disjunction A OR B truth table has A , B , and A OR B but mine has A ,B C, with A or B or C could some please explain this
Bradlee Stromatt
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Boolean Algebra expanding using absorption

Hi I have a question regarding the absorption law. I was told that I cannot expand ab = ab + abc by writing ab = ab(1+c). However, I believe you can expand xy = xyz' + xyz by doing xy = xy(z' + z) . Why does it work in this case and not the other…
Khoi
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