# Questions tagged [boolean-algebra]

The tag has no usage guidance.

216 questions
Filter by
Sorted by
Tagged with
8 views

### Which of the boolean expressions is a max-/minterm?

I have a exercise where I have to decide whether a term is a max-/minterm and reduce the expression to its corresponding max-/mintern or neither of them and for the following expression I do not know ...
9 views

### How to combine multiple Boolean Functions in CDNF efficiently for implementation on a CPU?

I am trying to see how fast I can implement a 6-bits to 6-bites lookup table. Generally, I am attempting to do this by using the common method mentioned in CS textbooks of using the Quine-McCluskey ...
16 views

### Prove the boolean function E = F + G contains of the sum of the minterms of F and G

I'm given a boolean function E which is result of the sum of F and G (Where both F and G are boolean functions for sure). By using K-Map I can easily understand why E would have the sum of the ...
19 views

### is duality principle in boolean algebra is true for every expression

Let say A = 1 and B = 1 and then A+B = 1 now by using duality(replacing or gate by and gate and 1 by 0) we can say that, A.B = 0 but this is not 0, because 1.1 = 1, so please anyone clear my ...
34 views

### Circuit complexity of hardest monotone function

Show there exists a monotone function $f\colon \{0,1\}^n \mapsto \{0,1\}$, such that the minimal size of a monotone circuit that computes $f$ is $\Omega(2^n / n^2)$. Use the fact that the number of ...
26 views

### Karnaugh Map: does maximal overlap always produce simplest boolean expression?

Suppose I have a 4x4 Karnaugh map with a few cells that are don't cares, and there are two ways of producing 3 groups of 4 cells. One of these ways overlaps groupings more that the other. Is one way ...
191 views

### Can every sentence of first-order logic be converted into an equisatisfiable equation in Boolean algebra?

There may be some theoretical literature, unknown to me, that addresses this question. If possible, I would like a practical approach to this problem. My attempt involves the use of an equational ...
24 views

11 views

### K Maps: Getting simplified boolean form

I have been trying to work out the simplest Boolean form for the following K-map: I get the following expression: (x2 AND X3) OR (x1 AND x2) OR (x0 AND x2) However, via Boolean algebra, I get (x3 OR ...
24 views

### Which gates are “pre computation” universal?

In the following, by “functions” I will mean 2 input 1 output Boolean logic functions (for conciseness). A function is called “universal” if by using it (sometimes multiple times, chained together), ...
29 views

### Simplification of a multi-index Boolean expression towards computation in fewer steps

Let $x_{ij} \in \{0,1\}$, $1 \leq i \leq M$ (typically, $M = 2000$), $1 \leq j \leq N$ (typically, $N = 10$), be Boolean variables. If possible at all, I would like to simplify the following ...
150 views

### Addition, multiplication, and apostrophe used to represent boolean algebra expressions?

I'm looking at a worksheet that expresses boolean logic expressions using multiplication, addition, and apostrophes; something I've never seen before. I can make a guess that the apostrophe is ...
72 views

### All 16 Boolean Logic Gates

I was doing some reseach and I came across a website that had listed 16 different boolean logic operators. I was wondering if all of them were real, and if so, what do they do. https://www....
35 views

### Significance of quantifier ordering in quantified boolean formulas (kQBF vs. QBF)

I am studying solvers of quantified boolean formulas (QBF) as a generalization of SAT solving. The standard DIMACS format of SAT specification is extended to QDIMACS, which adds "a ..." and "e ..." ...
93 views

### Does the naive conversion of a Boolean Formula to CNF have a polynomial or exponential complexity?

I am reading the naive conversion to CNF, this procedure is explaining in this book book, but I have not found a conplexity analysis of this algorithm: elimination of equivalence Elimination of ...
57 views

### Simplifying the Boolean expression $A + \bar{A}\bar{B}$?

So I'm trying to simplify the Boolean expression (1) $A + \bar{A}\bar{B}$. I noticed that by Karnaugh maps this is equivalent to $A+\bar{B}$, and I also noticed that if I take the complement of (1), ...