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 .

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Are there any Boolean function that helps to identify the block in the sequence.

consider a bit stream $$S = 000,010,100,111,011,001,101,110,011,110,111 $$I divide these in to two bit streams(blocks) $$000,010,100,111,011 $$ $$001,101,110,011,110,111 $$ now is there any Boolean function or any other criteria that given S I…
User1086
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Boolean Expression Simplification Error. Results not matching with the given results.

I was simplifying the expression: (K.(K.(J+L))')+(K'.(K.(J+L))) =(K.(K'+(J+L)'))+(K.K'.(J+L)) =(1+K.(J+L)')+(J+L) =(1+K.(J'.L'))+(J+L) =1+K.J'.L'+J+L However, when I was evaluating this Simplified expression using the truth table, the result did not…
MsBonniePython
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Is a complete Boolean $\sigma$-algebra ccc?

A Boolean $\sigma$-algebra that satisfies the countable chain condition (ccc) is complete. Is the converse true, i.e., is a complete Boolean $\sigma$-algebra ccc? If not (which is probably the case), what would be an example the complete BA which is…
Hugh
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Boolean algebra simplification proof without truth table

How to prove that $A\bar B+(\bar A + B)C=A\bar B+C$? I don't even know how to start. The distribution law doesn't help. All other laws are not applicable. Similarly, how to prove that $AD+B\bar D+C\bar D+A\bar C+\bar A\bar D=A+\bar D$?
eMathHelp
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Need help to understand a step to simplify this boolean expression

Looking my professor steps to simplify a boolean expression, he went from $$A'(B+C)(A+B)C'+B'$$ to $$A'(B+C)BC'+B'.$$ I've been trying to understand how did he do that but I can't. Can anyone help me clarify how this step was done?
Lucas Brodersen
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Multiply the number $(1001)_{2}$ by 3 digit number

I want to multiply the number $(9)_{10} \rightarrow (1001)_{2}$ by a 3 digit binary number. 1) How I can extract the boolean equations? 2) Make a circuit of it. so what I did is just see what happen if I multiply it, for example: $$(1001)_{2}*…
Ofir Attia
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Let $D_{m}$ be the divisors of m. Defins inf{a,b} = gcd{a, b}, sup{a, b}= lcm{a, b}, and -d=m/d. Investgate when $D_{m}$ is a Boolean algebra.

I Was preparing for my exam and wanted to write Formal Prove, Question: Let $D_{m}$ be the divisors of m. Defins inf{a,b} = gcd{a, b}, sup{a, b} = lcm{a, b}, and $¬\,d=\frac{m}{d}$ . Investgate when $D_{m}$ is a Boolean algebra. Here is my…
D0mBas3
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Show that a mapping from one Boolean algebra to another which preserves the operations ⊕ andʹ also preserves the operation ∗.

how do I show that the operations are preserved when mapping from one Boolean algebra to another. Since no Boolean algebra function is actually given. Thus how do I show this?` I believe Boolean isomorphism preserves the operations but then how do…
lives_in_virgosupercluster
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Can a Karnaugh map be solved in more than one way?

So I understand for doing a simplification by a K Map I should group my 1's (or even 0's) in $2^n$ elements, always trying to grup as much elements as possible. And I can group even adjacent elements .... So let's say, is it correct if I perform 5…
diegoaguilar
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Logic Circuit Question

1) Write the boolean expression after every GATE 2) Write the boolean expression of GATE 3 3) Try to simplify the boolean expression of GATE3 I need to know if what I did its right + your advice if there is another way to answer those…
Ofir Attia
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Converting a boolean expression to nand gates

Let f(x,y) = x.y + x.ycomplement. I want to convert this into nand gates. Although this is simply x I am not sure how to convert this into a NAND gate. which is generally done using DeMorgan's law
pensee
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Simplification of of Boolean expressions

I have been tasked to simplify the following boolean function of three variables $$f(x,y,z) = xy\bar{z}\vee \bar{x}\bar{y}\vee\overline{x\vee y\vee z} \vee xyz $$ The notation is such that $xy$ means $x\wedge y$. I believe that the most simplified…
Lim Cheng Ang
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Simplifying an 8-bit boolean expression

I am asked to find a minimum SOP implementation of a Hex to Braille code converter. Assuming my truth table is accurate, and D stands for "Don't Care", an 8-bit K-map seems impractical. Are there any other tools for hand analysis other than basic…
richbai90
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Distributive Law in Boolean Algebra problem

Im practicing boolean algebra on the following problem (A+B)(¬A+¬B) In my textbook they apply the distributive property to get A(¬A+¬B)+B(¬A+¬B) Im not quite sure how this is being applied and would appreciate some clarification. I know the…
Ummayair Ahmad
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Is the author's truth table incorrect or is my understanding of the order of operations wrong?

To understand enough about Karnaugh maps to solve this problem on 4Clojure (which hosts problems for the programming language, Clojure), I've studied the wiki articles on K-maps, Boolean Algebra, Set Theory, sets, disjoint sets, math notation,…
Aaron Bell
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