Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Questions regarding Boolean algebras as structures, or regarding functions defined from/to Boolean algebras fit into this tag very nicely.
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1answer
112 views
Infitive distributive law in boolean valued models
I'm posting the problem 2.14 and 2.15 of the book "Set theory" of J.L. Bell. These problem are proposed after the forcing relation chapter and I'm new in this kind of stuff, so I have some little ...
2
votes
1answer
102 views
Better compression for a positive DNF than via BDD
I am experimenting with compressing positive disjunctive normal form (DNF).
When I use binary decision diagrams (BDDs) related algorithms I don't get
very good results. For example the algorithms ...
2
votes
1answer
93 views
Non-Boolean group with every element of order two
Let $G$ be a group (not necessarily finite) such every element of $G$ has order 2. Every such group is abelian [1].
Clearly, every Boolean algebra $B$ is a group of this type,
when equipped with the ...
1
vote
1answer
119 views
Boolean Algebra on Circuits
Can I use boolean algebra to simplify electric circuits installed on buildings, establishments (etc.) using the blueprint of the buildings fluorescent lamp circuit system and electric fan circuit ...
1
vote
1answer
74 views
Transforming statements of a query language to propositional logic
I have a custom query language which expresses containment relations between variables. Containment in this context is simply an object (A) in programming language X (java/C#/python etc: a language ...
0
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1answer
63 views
How can you design a 3 bit adder using a 4 bit adder?
How can you design a 3 bit adder using a 4 bit adder?
The description and/or the circuit's scheme would be great.
0
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1answer
41 views
Memory and bits. Need some help
Could someone check over my answers to verify I am correct.
Say we have a memory consisting of 2048 locations, and each location contains 16 bits.
◦ A) How many bits are required for the address? ...
0
votes
1answer
148 views
Simplify the following expression using Boolean Algebra into sum-of-products (SOP) expressions
Simplify the following expression using Boolean Algebra into sum-of-products (SOP) expressions
$Q.S.U + (Q' + S').(R + V) + U.(R + V) + Q' + S.T.U$
$.$ = AND
$+$ = OR
This is what I have so far
...
0
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1answer
114 views
The input represent a 4-bit unsigned binary number, the output W, is 1 if the number is multiple of 2 or 3 but not both.
I completely understand how to make a truth table and the entire concept of boolean algebra. However, I am confused how to make the truth table for the above information. Because the input is a 4-bit ...
5
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0answers
76 views
Non-isomorphic countable Boolean algebras
I'm trying to solve the next exercise:
Construct a sequence $\mathcal{B}_0,\mathcal{B}_1, \ldots$ of countable Boolean algebras such that for all $m \neq n$ then $\mathcal{B}_0 \ncong \mathcal{B}_1$.
...
2
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0answers
27 views
Inferring simplest method to convert bit array 1 to bit array 2.
Consider the set of all bit arrays of length $n$. Now consider the set of all 1-to-1 functions that map from this set to this set.
Now select a single function out of the latter set. Is there any ...
2
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0answers
37 views
Basis of a Boolean Algebra
I have a construct that I proved forms a (finite) Boolean Algebra of sets over a given universe.
My questions are as follows:
Do I immediately know that there exists a unique basis for it?
If yes, ...
2
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0answers
122 views
Boolean Algebra Manipulation/Simplification
I have come across a couple questions while doing my digital logic work.
1) Is it possible to simplify these, while keeping each a product of sums? (I'm leaning towards no--the only way I could see ...
2
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0answers
50 views
Name for this type of space over a boolean algebra?
The structure has two carrier sets $E$ and $A$, operators $({}^*, \wedge)$ over $E$, and a ternary "decision" operator $D:E \times A \times A \to A$, written infix $(p?a:b)$, whose intended meaning is ...
2
votes
0answers
206 views
bent and hyper-bent boolean functions
Is the AND logic function considered to be a bent function. If so, how would you make a hyper-bent function using logic gates? Thanks!
1
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0answers
54 views
Showing that a Boolean algebra is a Boolean ring
I've proved that a Boolean ring is a Boolean algebra but I am having trouble with the converse. The operation for + is defined as the symmetric difference for elements $a$ and $b$ from the Boolean ...
1
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0answers
142 views
Find number of solutions to equation with dependent variables
Please help to find number of solutions of this equation
$y_{1}\vee y_{2}\vee\ldots\vee y_{k} = \varphi (x_{1},x_{2},\ldots,x_{n})$
where $y_{i}=y_{i}(x_{1},x_{2},\ldots,x_{n})$ is Boolean function ...
1
vote
0answers
92 views
When to Stop Simplifying a Well-Formed Formula?
I mean simplifying a wff(well-formed formula)in which, only $\lor$, $\land$, $()$and $\lnot$ are allowed, as minimizing the occurence of connective symbols( $\land$ and $\lor$).
It's self-evident ...
1
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0answers
44 views
Inverse function in multi-valued logic through the Webb function
Let Webb function in multi-valued logic as $Webb(x, y) = W(x, y) = Inc(Max(x, y))$. There is a theorem about any function in any multi-valued logic can be represented through the Webb function.
Then ...
1
vote
0answers
44 views
Generating Input Binary Combination Dynamically
this is probably right forum to post this question
I am currently working on a application where there is a requirement to generate binary combination of input signals in a truth table.
The signal ...
1
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0answers
55 views
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
...
1
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0answers
54 views
$\Delta_0$-formulas in the Boolean-valued model $V^B$
I want to show that $\Vert \check x = \check y \Vert = 1$ implies $x = y$, where $\check x$ is the canonical name for $x$ in $V^B$.
I'd like try induction over the ranks of $\check x$ and $\check y$ ...
1
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0answers
92 views
boolean algebra how can i prove a theorem
In a set of lattice in boolean algebra how can i prove this:
$$x \cdot (y+z) \ge (x\cdot y) +(x\cdot z)$$
1
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0answers
153 views
Can the reduced product construction generate boolean-valued models?
In model theory, the reduced product construction contains a collection of structures or models, a set I that indexes the collection, and a filter U on I. Ultraproducts are a special case of reduced ...
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0answers
21 views
A problem on duality of boolean algebra
A Boolean function $f_1^{D}$
is said to be the dual of another Boolean
function $f_1$ if $f^{D}_1$ is obtained from $f_1$ by interchanging the operations
$+$ and $.$, and the constants $0$ and $1$.
A ...
0
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0answers
31 views
Karnaugh map question $\displaystyle \sum_{} (2,3,6,7) $
I can't write here the map of Karnaugh of this function so I just ask whether this reduction goes after Y?
$F(w,x,y) =\displaystyle \sum_{} (2,3,6,7) $
In addition if there are two functions like: ...
0
votes
0answers
17 views
Write the following functions in algebraic sum of multiples or multiplying Amounts. If possible,simplify the expression
Write the following functions in algebraic sum of multiples or multiplying Amounts. If possible,simplify the expression
The Question is:
$F(A,B,C): Maxterms(4,5,6,7)$ :
$M4 = 100 => A'+B+C $
...
0
votes
0answers
14 views
What is the order of steps when simplifying functions with NOT
What is the order of steps when simplifying functions with NOT
I need advice on simplifying the following function, I have a function with several stages of NOT, Do I followed the steps?
Thanks!
0
votes
0answers
46 views
Is the choose function polynomial?
I have this problem which is described as follows:
Input:
You are given a multi-set M (a set that can contain duplicates), and two numbers P and T.
$ M = {(x_1,y_1), (x_2,y_2), ..., ...
0
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0answers
59 views
M-generic, transitive model and Boolean-valued model
$M$ is defined as a model of ZFC set theory. This
is Boolean-valued model question: how does one
prove that ultrafilter $U$ being M-generic leads to
the fact that $M^{\mathbb{B}}/U$ has isomorphic ...
0
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0answers
34 views
Booleans: Solve Algebraically
Prove using Prove algebraically :
1) x'′⊕ y = x⊕y' = (x⊕y)'
2) x⊕1 = x'
3) x⊕x' = 1
4) (A+B)(A'C'+C)(B'+AC') = A'B
$(A+B)(A'.C'+C)(B'+AC)' = A'B$
I know x⊕y = xy'+x'y But how do i deal with X'⊕Y? ...
0
votes
0answers
60 views
Representation of Boolean algebras
Stone's representation theorem states that every Boolean algebra is isomorphic to an algebra of point sets.
Loomis-Sikorski theorem states that ''every $\sigma$-complete Boolean algebra is ...
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0answers
56 views
Truth table for X = A.(B+C)'?
I have been beating my head on this for hours. I'm pretty certain that I've done it correctly, but my Quartus II simulation seems to disagree.
My Boolean expression: X = A.(B+C)'
My truth table ...
0
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0answers
43 views
Question regarding implicant chart of Quine-McCluskey algorithm
In https://en.wikipedia.org/wiki/Quine-McCluskey#Example, at the end of Step 1, there is a table that shows the number of 1's, minterms, 0-cube and size-2 implicants and size-4 implicants. But I am ...
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0answers
131 views
How to increment number using Half Adder ONLY?
I need to increment a number by using Half Adder Only.
I'll explain:
I'm getting 4 on/off switches, And I need to display how many switches are on.
How to do so?
I'm using CEDAR Logic. I really ...
0
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0answers
53 views
Prime implicants
Are prime implicants prime in the sense used for elements of rings?
That is: is boolean algebra done in a ring? It seems like it is, one with the elements from Z mod 2z and + such that a + a = a. In ...
0
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0answers
63 views
Need to know XOR properties?
I have a set of numbers $\{a_{1}, a_{2}, a_{3} , a_{4},....a_{n} \}$ where $1\leq n \leq 10^{5}$.
Now the sum of the interval $[1,4]= a_{1}+a_{2}+a_{3}+a_{4} = S$,
then i do this operation $a_2$ ...
0
votes
0answers
34 views
Boolean Function
A Boolean expression is given: (A B)’ + B C’ +A’ C = F.
Construct the logical circuit and draw the timing diagram of the output F.
I am not sure where to start.
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0answers
37 views
Generalization of many-values logic minimization
What approaches of ternary and many-valued logic minimization algorithms (for example, Quine–McCluskey or Karnaugh map) are exists?
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0answers
125 views
Simplification of a Product of Sum equation from a truth table
I am trying to simplify an equation which was derived from a truth table using the Product of Sum rule and I need help simplifying it to match to a certain equation. The truth table is linked and I've ...
0
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0answers
75 views
Given a state transformation matrix and a state vector, how to find the total number of changes for each individual element.
I have a vector of binary variables, $s$ representing a state at some point in time, and a transformation matrix $T$. The initial state is $s_0$.
$s_n = Ts_{n-1}$
Given a number of transformations, ...
0
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0answers
143 views
homework: number of canonical expressions
There is a question:
What is The number of canonical expressions that can be developed over
a 3-valued boolean algebra?
I was trying to solve this. Canonical expression is the combination of ...
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0answers
57 views
Simplify $f=Σ(8,12,13,14)+dΣ(3,7,9,10)$
I was doing this question of boolean algebra,
Simplify $f=Σ(8,12,13,14)+dΣ(3,7,9,10)$ using Karnaugh map.
Can anyone please tell me what is $d$ in this question?
I know its a stupid question ...
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0answers
14 views
Formalizing many-valued logic function
How would one correctly define a many-valued logic function that:
gets as input N variables (values range from 0..100)
returns 0 unless N/2 variables have a value $\ge 50$
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0answers
134 views
Creating a System of Boolean Equations, “Reverse Gaussian Elimination”
I have an idea for a game I'm developing where logic puzzles are randomly generated for the player to solve. For example:
...
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0answers
59 views
Standard references for boolean algebra?
I'm wondering what books are considered standard references these days, for boolean algebra. I have:
Givant & Halmos, Introduction to Boolean Algebras (2010);
Sikorsi, Boolean Algebras (3rd ed., ...
0
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0answers
121 views
Truth Tables for Hyper Bent Functions
Could anyone supply me with an example of a truth table for a hyper bent boolean function? The fewer the number of variables the better. Thank you!
0
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0answers
43 views
Create treshold-rules from an array
I don't know if I will be lucky... I am quite in a hurry, and I would need some advice.
First the picture I made so that I can explain my question more easily:
A) I do not need a good working ...
0
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0answers
82 views
Single Complement Variable + 1
Is a complement + 1 = 1? For example A' + 1 = 0;
I was thinking it was (I'm new to boolean algebra) since A' = 0, and 0 + 1 in boolean algebra is just 1. Of course, A can be anything, but assuming ...
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0answers
190 views
How many presentable boolean functions with n attributes are linear separable?
The aim is to find a formula for the question.
For n=2 i get (2^(2^n)=16 possible functions.
This is the solution for a boolean function with 2 attributes:
...
