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
0
votes
1 answer

How to solve Boolean Expression

im struggling with this Boolean expression. If anyone could help me solve it that would be great, I've been struggling with this for over a week now and would really like someones help. https://i.stack.imgur.com/DjLwy.jpg
DarkArmy
  • 3
0
votes
2 answers

I must solve this by using boolean algebra rules but i dont know how

I've got this problem there which I have no idea how to solve (by using boolean algebra rules). $$ b\bar{c} + ba + \bar{a}\bar{c} $$ I have to simplify it and I don't know which rule should I use.
Zdenda
  • 1
0
votes
2 answers

How do I interpret this Boolean expression

Please help me to understand this Boolean expression: $$1 < a_i < 10^6$$ My first guess is this: One less than a modulo i and also less than 10 to the 6th power. Is my interpretation correct? For context, this is part of a constraint to a problem…
Necromancer
  • 103
0
votes
3 answers

How to establish that two Boolean expressions are the same by transforming one into the other?

I'm trying to figure out what rules I need to manipulate $A + B'D + B'C + A'BD' $ into $A + B'D + BD' + CD'$ The first I derived from the output of a combinational circuit, the second from entering the output into a K-map. I plugged these two…
Werewoof
  • 325
0
votes
1 answer

Need help simplifying a boolean expression using algebraic theorems/postulates only

Suppose I have this boolean expression: W'XYZ + WX'YZ + WXY'Z + WXYZ' + WXYZ How would I go about simplifying this without using a K-map? Using K-map, the simplified form is XYZ + WXY + WXZ + WYZ. I read about the redundancy theorem somewhere, would…
Sanchit Batra
  • 3
0
votes
1 answer

Boolean simplification of y(x' + (x+y)')

I've been trying to perform Boolean simplification on the following expression: $y(x' + (x+y)')$ So far, my steps have been: $y(x' + (x+y)')$ $y(x' + x'y')$ $y(x' + x')(x' + y')$ $(yx')(x' + y') $ I have no idea where to go from here. I feel as if…
Derrin
  • 1
0
votes
1 answer

Did I simplify the boolean expression correctly?

I wanted someone to check and make sure that I did this right, I'm hoping that I did but if I didn't, please point me in the right direction of where I went wrong
AceNinja1101
  • 15
0
votes
1 answer

Implementing $AB\bar{C}D+A\bar{D}+\bar{A}D$ using only AND & XOR gates

Question: Implement $F(A,B,C,D)=AB\bar{C}D+A\bar{D}+\bar{A}D$ using only AND & XOR gates My try: I know that $A\bar{D}+\bar{A}D$ functions like a XOR gate which takes $A$ and $D$ as input. But then I don't know what to do which the part…
Arman Malekzadeh
  • 4,108
0
votes
1 answer

Boolean algebra - sum of products form

I have a logic circuit where the output can be represented with the following boolean expression (1)$\overline {xy}$ + x $\bar y z$ + $\overline {\bar x + z} $ + y Using truth tables I found the complete sum of products form as: (2)$xyz + xy \bar z…
bosra
  • 561
0
votes
0 answers

simplify boolean expression using consensus theorem

How to simplify this Boolean expression using consensus theories? f(x,y,z) = xy + xy’z + y(x’+z) + y’z’
Biyan Alya Safira
  • 3
0
votes
1 answer

Can a statement with all AND statements have a Disjunctive Normal Form?

If I have something like: p AND q AND r AND s Is there a way to rewrite this in Disjunctive Normal Form?
Human Cyborg Relations
  • 189
0
votes
0 answers

Is a clause "A" a tautology if and just if it contains both the atoms p and ¬p at the same time?

I'm just starting boolean algebra, and I'm kind of stuck here. I know $A=(p \text{ or } ¬p)$ is a tautology, and what I've tried to do is to find an example of a tautological clause that does not include $p$ or $¬p$ at the same time, without…
Chus
  • 1
0
votes
2 answers

Can Known Conditions be Used to Make Assumptions About Equality in Boolean Algebra?

I'm attempting to prove equality between $(x+z)\bullet(\neg x + y) \bullet (y+z) = y \bullet z$ With the known conditions $x \bullet y=0$ and $x+y=1$. Using the known conditions, we know that one variable, $x$ or $y$, must be equal to $1$ and the…
Zulfe
  • 289
0
votes
1 answer

Simplifying this Boolean expression

How do you simplify this expression? $$\lnot[\lnot[(P \lor Q) \land R] \lor \lnot Q] \equiv Q \land R$$ I understand the laws used but still not getting the exact answer. I would appreciate if someone solved this for me.
gheeees
  • 3
0
votes
1 answer

K-map & Boolean Expression

After obtaining the result from Karnaugh map: $$F = ad+a'b'c'+a'b'c$$ Can I still further simplify the expression to: F = ad+a'b'c'+a'b'c = ad+a'b'(c'+c) = ad+a'b' or should I just leave it as how it should be?
BEX
  • 37
1 2 3
…
64 65