# Questions tagged [boolean-algebra]

The tag has no usage guidance.

216 questions
Filter by
Sorted by
Tagged with
795 views

### Karnaugh map with don't care: increasing the number of groups instead of simplifying

AB 00 01 11 10 00 | x | 1 | 0 | 1 | CD 01 | 0 | 1 | x | 0 | 11 | 1 | x | x | 0 | 10 | x | 0 | 0 | x | The answer to the ...
201 views

### Can the Euclidean distance function be computed using only XOR's

The Eulidean distance function $d$ of $x$ and $y$ is given by: $d(x,y)=\sqrt{x^2-y^2}$ Let us assume that $x$ and $y$ are fixed-point numbers, or $x,y$ are element of some subfield $f_n$ of $F_p$. ...
52 views

### What is the current state of research on the representation of boolean functions using wavelets

The harmonic representation of boolean functions such as XOR or AND has been studied in different course note lectures that can be found on Google. http://cs.mcgill.ca/~hatami/comp760-2011/ http://...
246 views

### Is my simplified explaination of the XOR swap correct?

The XOR swap is a well-known in-place algorithm to swap two values, by XOR:ing them bitwise. It goes as follows: a = a ^ b b = a ^ b a = a ^ b Now, I was ...
141 views

### What is the state of the art in efficient boolean function operations?

How do you most efficiently combine boolean functions with a large number of variables using AND, OR, and NOT? The most up-to-date work that I can find on this subject is about 20 years old (...
46 views

### Reducing a system of two boolean algebra assertions to a single one

Given a system of two Boolean Algebra equalities a = b. c = d. one can exhibit a single equation F(a,b,c,d) = 0. which is ...
119 views

### Simplifying circuits using boolean algebra

I am having a lot of trouble simplifying my circuit using boolean algebra. I am very new to this and any explanation would be greatly appreciated. I have y'+z+w'x+wx' I feel like I could use DeMorgan'...
2k views

### Are Boolean functions Turing complete

A Boolean function is a function $f:\{0,1\}^n\rightarrow\{0,1\}$. The boolean basis $(\vee,\wedge)$ is known to be Turing complete as it allows any sequence $s\in\{0,1\}$ to be flipped or to be left ...
84k views

### Which law is this expression X+ Xā.Y=X+Y

Question. Name the law given and verify it using a truth table. X+ Xā.Y=X+Y ...
201 views

### Finding a graph-theoretic representation of expressions in Boole's algebra

I just read "Boole's Algebra Isn't Boolean Algebra" by Theodore Halperin (behind a paywall here). I don't have a strong background in abstract algebra, so, frankly, the paper is a bit over my head but ...
1k views

### Odd Parity Function [closed]

I am trying to define a Odd Parity Function that takes three 1 bit inputs and will output a 1 if the 3 bits are odd as a Boolean function. ...
127 views

210 views

### Recognizing Horn clauses

I am currently studying model theory and I am trying to decide if a clause is a Horn Clause. I know that a Horn Clause is a clause with at most one positive literal, but there are some clauses that it ...
$$(\neg A \wedge \neg C) \vee (\neg A \wedge D) \vee (\neg A \wedge B) \vee (\neg B \wedge \neg C)$$ can simplify down toĀ  $$(\neg A \wedge D) \vee (\neg A \wedge B) \vee (\neg B \wedge \neg C)$$ ...