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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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Boolean Algebra - Xor simplification

I have a boolean equation: $e(g \oplus (g + b))$ and it is simplified to $e(\lnot g)b$. I do not see how this simplification is done. What i did was the following: $e(g \oplus (g + b)) --> e(g(\lnot(b+g)) + (\lnot g)(b + g))$ $--> e(g(\lnot b) +…
Noobgineer
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Simplifying a Boolean algebra equation

I have a boolean algebra equation that i'm not able to simplify fully. \begin{align} &(c+ab)(d+b(a+c))\\ &(c+ab)(d+ba+bc)\\ &cd+ abc + bc^2+abd+a^2 b^2 + ab^2 c\\ &\text{using boolean laws $x^2=x$ and $x+x=x$}\\ &cd + bc + abd + ab + (abc + …
Allstar
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Implement boolean function with OR-NAND and NOR-OR gates

This is the boolean function: F(A,B,C,D) = Σ (0,4,8,9,10,11,12,14) and so after using a K-map to minimize it, I came out with F(A,B,C,D) = C'D' + AB' + AD'. Now the other two parts of the problem were representing it with AND-NOR gates and NAND-AND…
move_slow_break_things
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Simplify the boolean function below by using algebra laws.

I've been stuck on this question for some time, if anyone happens to solve it please explain step by step. $$(A +B ) \times ( A' + C ) \times ( B + C )$$
GhettoBurger
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Can you simplify this Boolean expression any farther?

I was working through a problem for a Computer Engineering course and i was given this logic function F(A,B,C,D) = ~A~BC~D + ~AB~C~D + ~ABC~D + ABC~D After factoring out BC~D from two of the terms and getting (~A + A) = 1 *(BC~D) I got F(A,B,C,D)…
Dylan Steele
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Help with Boolean expression simplification with $4$ variables.

I've simplified this expression and am unsure if it's completely simplified. If it can be simplified, can you provide me with the answer and the steps/laws taken to do so? Thank you. $y’(z+x)+z’(xw+x’y)$
Jim
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I need prove a boolean function

In need to prove with boolean algebra that XOR complement (negado) is equal to XNOR but i cant do it, can you help me? !(!xy+x!y)=xy+!x!y how to prove it?
Schiffer
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Brackets in Boolean ALgebra Distributive Law

What is the purpose of the brackets in all the examples I've seen of the distributive law? Why are there no brackets when distributing an AND term and there are when distributing an OR term? Could I write: X * (Y + Z) = (X * Y) + (X * Z)? eg of law.…
DAnsermino
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How to show that $f(w,x,y,z)=wx'y'+xz+w'x'y$ isn't universal?

First, I will note that I don't need a formal prove. short explanation is enough. The only way I know to show that an operator isn't universal, is by showing that you can't implement $NOT$ with it. This worked for me so far, because I solved only…
Rodrigo
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What do you call 2 boolean functions which are equivalent if two arguments exchanged?

What do you call boolean functions which are identical accurate to argument order? EDIT1 I meant not symmetric function. I mean, for example, implication function with truth table 00=1 01=1 10=0 11=1 and the function 00=1 01=0 10=1 11=1 i.e. giving…
Suzan Cioc
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Finding the principal disjunctive normal form (PDNF) of a Boolean expression

Find the principal disjunctive normal form (PDNF) of a Boolean expression $$((p\wedge q) \rightarrow r)\vee((p\wedge q)\rightarrow \neg r).$$ I tried by expanding it but I am stuck with the expression $(\neg p \vee \neg q \vee r) \vee (\neg p…
Balaji
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Boolean Algebra Product of Sums

I have a question to solve the following expression and get it in terms of product of sums (AB' + A'B)C And I tried taking the compliment of this [(AB' + A'B)C]' [(AB' + A'B)' + C'] [(AB')'.(A'B)' + C'] [(A' + B).(A + B') + C'] [(A' + B +…
Padmal
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How many minimized forms can a boolean expression have with 4 variables?

I have this theoretical question I can't get my head around. Assuming I have a function (any function) with 4 variables, and I draw a Karnaugh Map in order to extract the most simplified expression by selecting the correct PIs, how many possible…
shaqed
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Boolean Expression - ((a'.b)'+c')' + (a'+(b'.c)')'

I'm trying out one of the exercise, but not sure whether did I get the answer right, is the answer for the following output is 'C'? Kindly help to simplified it, as I'm not sure about it, still trying hard to learn. Simplify the following boolean…
user295889
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Can't simplify this boolean expression

I'm trying to simplify this boolean expression: $$(AB)+(A'C)+(BC)$$ I'm told by every calculator online that this would be logically equivalent: $(AB)+(A'C)$ But so far, following the rules of boolean algebra, the best that I could get to was this:…
shaqed
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