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
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Derive resultant Boolean function

The question goes as follows; Andreas, Benedikt, Carolin and Dora are invited to a party. Following are known: When Andreas goes, Benedikt goes as well. Carolin and Dora are not both going. Between Andreas and Dora at least one goes. When…
ro ko
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Boolean simplification

I'm trying to simplify the following expression: (x+ ~x)~(~(~z xor y) + (yx)) (1)~(~(~z xor y) + (yx)) ~(~(~z xor y) + (yx)) (~z xor y) + ~(yx) (~z xor y) + (~y + ~x) (~y~z + yz) + (~y + ~x) <---- im stuck here How can I simplify…
Cesa Salaam
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Simplify this boole algebra expression

Can someone help me with this expression, and how to simplify that with all steps? Im kind of lost in those, and i have exam in 2 days. Thank you Expression The result of expression is: F = B + C * A'
ItzMeN0n
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Karnaugh Map result = Using principles ?

Does using Karnaugh Map produce same result as using principles to simplify boolean expression?
Donny Avaris
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Reduce boolean algebra

I have to reduce this boolean algebra : ((x⊕y)⊕(y⊕z))⊕(x⊕(1⊕((y⊕0)⊕z))) I found out that ((x⊕y)⊕(y⊕z)) = x⊕z y⊕0 = y 1⊕(y⊕z) = negative(y⊕z) looking at the solution it must be reducable to negative(y), but i don't know how to get from …
epoyraz
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Using Redundancy to Simplify Boolean Expression

I came across a question which I need to solve using Redundancy: x'z + x'y + xy'z + yz Could anyone help me solving this? I must solve it using Redundancy only...
Donny Avaris
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Boolean expression to be converted in a NOR-only way

Guys I need to convert an expression using AND, OR and NOT to an expression using only NOR. However I'm not being able to do it algebraically. Can someone give a hint on how to start. I already tried to complement the expression and then to apply De…
Granger Obliviate
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Pass a logic function using only NAND

So I had a truth table and using a Karnaugh map I simplified a function. I obtained. $ f = \overline{A_3}A_2\overline{A_1} + \overline{A_2}\overline{A_0} + A_3\overline{A_0} $ Then using the distributive property of boolean algebra: $ f =…
Granger Obliviate
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Stuck on simplification of K-map

I've been stuck with this problem because I don't know where I can go or where to start. $$F(w,x,y,z) =(x\land z)\lor(w\land\neg x\land\neg z)$$ I'm pretty sure I have to do this $$F(w,x,y,z) =(x\land z)\lor(w\land(\neg x\lor\neg z))$$ but from here…
CodeGorilla
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Rewrite $((p \land q)\lor(q \rightarrow(p\land \lnot r))$ to DNF

So, I'm a bit stuck here and I don't see how I can continue. I needed to write the following expression to DNF: $$((p \land q)\lor(q \rightarrow(p\land \lnot r))$$ What I tried: $$((p \land q) \lor (\lnot q \lor (p \land \lnot r)))$$ $$((p\land…
Adnan
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Karnaugh Map minimal SOP form

I have a hoemwork and must be done without boolean algebra Please simplify this function with K-Map only $F = ABC + A' . B . (A' . D')'$ I know this can be easily solve by using boolean algebra and I have tried it $F = A.B.C + A' . B . (A' .…
Unknown123
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Please help solving some Boolean Algebra problems

I want to know how these problems are solved. Thank you very much. i) x·y + y·z + x'·z = x.y + x'·z ii) (x + y)·(x' + z) = x·z + x'·y
Abhisek Mukherjee
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Simplifying a boolean algebra equation (A'B + AC + ABC' + BC)

$A'B + AC + ABC' + BC$ $A'B+AC+ABC'$ (Complement's theorem) Could I get a hint of where to proceed next? I've been going back and forth looking at theorems but can't understand how one would fit with all the different variables.
stumped
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How to simplify boolean expression

Can someone show me step by step how to simplify this boolean expression? I would like to learn how to handle this kind of simplifications: $$ Y = \neg(D \wedge\neg E) \vee (\neg E \wedge D ) $$ I can apply boolean laws for the first steps, that…
glc78
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Know the Boolean algebras order for Hasse Diagram

I have (F(B^2,B)) for the functions B^2 in B, defined by f#g -> f(x)<=g(x) for each x in B^2. I need to draw the hasse diagram for the boolean algebra (F(B^2,B),#), but don't know if is a order 3 like this: Hasse or a order 2. How can i know it?
El0din
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