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
-1
votes
1 answer

Simplifying Boolean algebra question

I'm not quite sure how to go about simplifying this boolean expression, any help would be great. X'Y'+X'Z'+Y'Z
Joe
  • 1
-1
votes
2 answers

boolean expressions simplification Help needed.

I am stuck simplifying. Can anyone help? It states that $$ (XY’+YZ)’ = X’Y’ + X’Z’+YZ’ $$ I tried all axioms yet I can't figure it out.
Request for New Parents Pack
  • 1
-1
votes
1 answer

is this boolean algebra transformation correct

I have the following expression: (A=1 or A=2) or (B=1 or B=2) and try to transfer it to: (A=1 or A=2 or B=1 or B=2) Are these two expressions equal?
walterhuang
  • 103
-1
votes
1 answer

Boolean logic simplification

To simplify $$ A'B'C'D + A'B'CD' + A'BC'D' + A'BCD + AABC'D + ABCD' + AB'C'D' + AB'CD $$ I have no idea how to start the first step. Thanks in advance!!
rMath
  • 81
-1
votes
1 answer

boolean algebra simplification for x(1 +bc') + x'(b' + bc)

in this equation using boonlean algebra: X(1 +BC') + X'(B' + BC). can i simplify (1 +BC') = 1 and (B' + BC) = B' +C? i used truth table and they have the same result, but i do not know how to solve it using the rules? thanks for all the help.
wanderer
  • 11
-1
votes
1 answer

function f(x) = x && x is unary or binary?

I am currently studying Boolean algebra, here is what I learned from school ( If I understand correctly): A Boolean function of one variable (input): unary boolean function. A Boolean function of two variables (input): binary boolean function. A…
Helen Guo
  • 55
-1
votes
3 answers

$\overline{(a+\overline{b})\cdot (\overline{a}+b)}$ simplification boolean algebra

For context: I am learning Boolean Algebra by myself for fun and one of the questions in the book I am reading was a long boolean expression and the task was to simplify it to be the XOR boolean expression. I have managed to come quite a bit but…
riemanneru
  • 69
-1
votes
1 answer

Is it true that in any boolean algebra $x\oplus0 = x$?

I was wondering about this question. Logically, I would like to say that in every boolean algebra that is true. Because: $x\oplus0=x·0'+x'·0 = x·0'$. And in the binary boolean algebra that is correct as: $0'=1 \rightarrow x·0'=x·1=x$ But is that…
Eatay Mizrachi
  • 401
-1
votes
1 answer

Boolean expression for sum of $n$ variables is equal to $k$

I am looking for a general formula/algorithm for the construction of boolean expression of $n$ variables which is true iff the sum of all variables is equal to $k$. I don't understand the second part of this post. Something like this in mathematical…
Jan Veselý
  • 111
-1
votes
1 answer

Simplify the notation a*a*b*b

I am trying to reduce the notation aab*b I believe ab^2 is the answer - can someone confirm I have it correct or give me the correct simplification Thanks
Jack Klosterman
  • 1
-1
votes
1 answer

What do "$m$" and "$d$" mean in the formula $F(A,B,C,D) = \Sigma m(9,10,12) + d(3,5,6,7,11,13,14,15)$?

What do "$m$" and "$d$" mean here? I know that "$\Sigma$" means sum of products but I do not know what "$m$" and "$d$" mean. Please help.
Abhiram M V
  • 13
-1
votes
1 answer

Proving that a given gate is universal

The question is: Given gate called NEW has 4 inputs and 1 output NEW(w,x,y,z)=zy(w+z) Is NEW is Universal logic gate? I found that the gate is not universal because I can't create NOT gate with it. How should I prove it? thanks
Felix
  • 3
-1
votes
1 answer

Boolean expression simplified

c. Interpret the following complex Boolean expression and produce a truth table and a logic circuit? (x+y•x) + (x•y) .=AND +=or
Callum Smith
  • 1
-1
votes
1 answer

Free (Boolean) $\sigma$-algebra on a denumerable set of free generators

The free Boolean algebra on a denumerable set of free generators is atomless and denumerable. In fact, it is up to isomorphic copies the only atomless denumerable Boolean algebra. Consider now the free (Boolean) $\sigma$-algebra on a denumerable set…
Beginner
  • 574
-1
votes
2 answers

Simplifying Boolean expression $(x′yz′)+(x′yz)+(xy′z′)+(xy′z)+(xyz)$ using DNF

\begin{array}{c|c|c|c} x&y&z&f(x,y,z)\\\hline 0&0&0&0\\0&0&1&0\\0&1&0&1\\0&1&1&1\\1&0&0&1\\1&0&1&1\\1&1&0&0\\1&1&1&1 \end{array} I think I have solved by half, but I can not completely simplify $$x′yz′ + x′yz + xy′z′ + xy′z + xyz\\ x′y(z′+z) + xy′z′…
Brian
  • 163
1 2 3
…
64 65