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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Boolean Algebra (Matrix?)

I am new to Boolean Algebra and I'd just like to know: Is it possible to encode boolean logic into a matrix such that successive powers of that matrix perform logical computations? For example, given $A$ and $A \Rightarrow B$, we can deduce $B$. Is…
Ben Crossley
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Absorption laws in Boolean algebra

Does anyone know how to prove the absorption laws in Boolean algebra? i.e. $$x + (x * y) = x$$ $$x * (x + y) = x$$ Thankyou so much
lasan manujitha
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How can this boolean expression be simplified?

I would like to have a step-by-step simplification of this boolean expression $\bar{x}\bar{y}\bar{z}\bar{w}+\bar{x}\bar{y}z\bar{w}+\bar{x}yz\bar{w}+\bar{x}yzw+x\bar{y}\bar{z}\bar{w}+x\bar{y}z\bar{w}+x\bar{y}zw+xy\bar{z}w+xyzw? $ I have…
Mathematics1990
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Converting Four Variable OR to NOR (using only NOR GATE)

I want to convert a four variable OR (i.e. OR(A,B,C,D)) to NOR. I did this using 6 two variable NOR like the picture below. but I think it can be done easier. Can anyone suggest any way to do this and avoid using this amount of gates. For example…
amir na
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$\bar{A}\bar{B}+A\bar{B}\bar{C} \equiv \bar{A}\bar{B}+\bar{B}\bar{C}$

When simplifying an expression I managed to get as far as the left hand side of the below. $$\bar{A}\bar{B}+A\bar{B}\bar{C} \equiv \bar{A}\bar{B}+\bar{B}\bar{C}$$ The answer was the right hand side. Without a truth table, I don't see how I could…
user496277
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Finding SOP form of function f

An exercise says : Use algebraic manipulation to find the mimimum SOP expression for the function $$f = x_1x_3 + x_1x_2' + x_1'x_2x_3 + x_1'x_2'x_3'$$ The given solution says: $f = x_1x_3 + x_1x_2' + x_1'x_2x_3 + x_1'x_2'x_3'\\ = x_1(x_2' +…
Κωνσταντίνος Κορναράκης
  • 455
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Problem finding SOP form of f + g

I have a project and I am asked to find the sop form of f+g and find its cost and then compare it to the cost if I implement f and g separately. I am trying to find SOP form of f+g and I am stack because f and g has nothing in common based on the…
Κωνσταντίνος Κορναράκης
  • 455
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Can any one help me solving this expression using boolean Algebra F=x'(y.z'+y'.z)+x.y'(y+x.z')

I have solved some expression but can't proceed further F=x'(y.z'+y'.z)+x.y'(y+x.z') =x'y.z'+x'.y'.z+x.y'.y+x.x.y'.z'(by distributive law a(b+c)=ab+ac) =x'y.z'+x'.y'.z+x.x.y'.z'(by using rule y'.y=0) =x'y.z'+x'.y'.z+x.y'.z'(by using rule x.x=x)
Alex Fernandez
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Simpler sum of products from boolean algebra than from karnaugh map

I was given a question, simplify the expression represented by the sum of minterms 0,1,3 and 7 for the 3 parameter function f. Writing this out I got $f = A'B'C' + A'B'C + A'BC + ABC = A'B' + BC$. However, using a karnaugh map BC 00 10 11 01 A 0 …
Ben
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Convert Boolean function to NAND-only using De Morgan's law

I have a function that I must convert to NAND-only. I've been trying to use the De Morgan's law but, I'm getting wrong results. Here is my function: $$z = \overline{d} \overline{f}(\overline{a}ce + ac\overline{e} + \overline{b}a\overline{c} +…
Nedas
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Is there a way to simplify of the next boolean expression?

Im trying to simplify the next expression $$A\bar{B}E+\bar{A}B\bar{E}$$ so the approach is to factor $E$ and ·$\bar{E}$ to get something like $$A\bar{B}+\bar{A}B (E+\bar{E})$$ (this step before is not allowed, so how to get last…
riccs_0x
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Proving uniqueness of solution in Boolean algebra

System: $a+x=1 \land a\cdot x=0$ has unique solution for x, for all values of $a \in B$. It is obvious that $x=a'$ is one solution , but how to prove the it is only one? I have tried assuming that there is another solution $b\neq a'$, but I keep…
Dovla
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Canonical Form Question

I have a quick question about some Boolean algebra. The problem is: F (A, B, C) = A + B And I want to expand it into canonical-sum form. The problem is there is no 'C' so I am unclear on how to do it. Normally, I would find the min-term and go…
Cyberboy1551
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Sum of product -

I am having some issue in minimize the following sum of products. My solution is: not A and not B or A and ((B and not C)or C) But I think it is not right.
Prova12
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Boolean Algebra proving algebraically simple

$$(X'+Y )(X+Y')=XY+X'Y'$$ I am just wondering how these are equal, and what laws are used to get there
Aaron
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