All Questions
15
questions
1
vote
0
answers
32
views
How to find values that generate a particular boolean expression
On question 1 of our homework we are asked to find which values of the boolean variables equate to the resulting boolean expression. I tried finding resources on how to complete this but I came up ...
- 11
3
votes
2
answers
145
views
Characterising functions $\mathbb{F}_2^n \to \mathbb{F}_2$ satisfying special equations
Let $\mathbb{F}_2=\{0,1\}$ be the field with two elements, and let
$u:\mathbb{F}_2^n\rightarrow \mathbb{F}_2$ be a function.
Is it possible that
$$
\sum_{x \in \mathbb{F}_2^n}(-1)^{u(x)+u(x+a)}= 0,
$$...
- 25.3k
4
votes
1
answer
183
views
Every boolean function is multiplicative with probability greater than $1/2$
Let $f:\left\{-1,1\right\}^n\to\left\{-1,1\right\}$.
How to show that
$$
P_{{x,y,z}} \{f(xyz)=f(x)f(y)f(z)\} \ge 1/2?
$$
where $x,y,z$ are distributed uniformly and independently on $\left\{-1,1\right\...
- 25.3k
3
votes
4
answers
79
views
how to prove $A+A'B+A'B'C+A'B'C'D=A+B+C+D$
Prove the above relationship by using the Boolean definition. I tried $A+A'B=A+B$, but end up with $A+B+A'B'(C+D)$, how can I go next?
- 61
2
votes
1
answer
47
views
Are bits defined in a Boolean ring?
Premise: I'm not a mathematician, please be patient.
Anyway, if I consider the Galois field $GF(2)$ and two operations $+$ (inclusive or, also denoted with $\lor$) and $\neg$ (negation), where, given $...
- 21
-1
votes
1
answer
42
views
Ordered Sets and Lattices
Recall the topic “Ordered sets and Lattices” that the set $D_m$ of divisors of $m$ is a bounded, distributive lattice with
$$a+b = a\lor b =\operatorname{lcm}(a, b)$$
$$ab = a\land b =\gcd(a, b)$$
(...
- 11
2
votes
1
answer
239
views
What is (mathematically) minimal computer architecture to run any software [closed]
Computer consist of hardware, literally hard wiring machine language instructions (operations) and operands to predetermined results. At the lowest level of interest, this hard wiring is physical ...
- 121
2
votes
1
answer
139
views
boolean algebra simplify using kmap
question: this is standar sop,try to simplify it using kmap
...
- 1,059
3
votes
1
answer
3k
views
What does a small circle operation between two matrices mean?
I'm working on an assignment for my Discreet Mathematics and Logic class, and we're learning about Binary Relations. One question I'm failing to understand involves determining the result of ...
- 585
0
votes
3
answers
217
views
Simplify the following Boolean expression.
Can someone explain to me how this step done? I got a different answer than what the solution said.
Simplify $x(y+z)(\bar{x} + y)(\bar{y} + x + z)$
what the solution got
$x(y+z)(\bar{x} + y)(\bar{...
- 27
0
votes
1
answer
1k
views
How to find logical equivalence?
Is the function $(∼p ∨ q) ∧ (p ∨ ∼r) ∧ (∼p ∨ ∼q)$ equal to the function $∼(p ∨ r)$?
Practicing out of a textbook for my test - I honestly have no idea how to simply this algebreically. If I had to do ...
0
votes
3
answers
13k
views
How many ways are there to sit 4 people from a group of 10 people around a circular table where two sittings are considered
How many ways are there to sit 4 people from a group of 10 people around a
circular table where two sittings are considered the same when everyone has the
same immediate left and immediate right ...
- 1,641
1
vote
1
answer
2k
views
How many binary bit strings of length 32 are there
How many binary bit strings of length 32 are there?
I think I know the answer but I'm not sure...wouldn't it just be $2^5$ ?
- 1,641
0
votes
2
answers
2k
views
What is the algorithm to add binary numbers with boolean operations? [closed]
What is the algorithm to add up two binary numbers using only boolean operations (negation, conjunction, disjunction) in linear time? Also the program flow needs to be "linear" as well, meaning there ...
- 1
2
votes
2
answers
123
views
Boolean Algebra-Simplification Assistance Needed
I have to show that (!(P.Q) + R)(!Q + P.!R) => !Q by simplifying it using De Morgan's Laws. Here is what I did but I'm not sure it's right.
(!(P.Q) + R)(!Q + P.!R) => !Q
(!P + !Q + R)(!Q + P.!R)
!(...
- 21