The binary tag has no wiki summary.
1
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1answer
84 views
Problem about BCH code
I have another homework to do, please give me some hints in order to solve this problem:
"Determine whether the dual of an arbitrary BCH code is a BCH code."
1
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1answer
101 views
Problem about narrow sense BCH-Code
I have an homework to do and i have no idea where to start. The question is:
"Show that a narrow-sense binary BCH-code of length $ n=2^m-1 $ and designed distance $ 2t+1 $ has minimum distance $ 2t+1 ...
2
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2answers
108 views
multiple xor (sum of parities)
If we have:
$b_1 \oplus b_2 = b_1 (1 - b_2) + b_2 (1 - b_1)$
what is (or are, if there are different versions) the compact general formula for a multiple "summation":
$b_1 \oplus b_2 \oplus \dotsb ...
1
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3answers
148 views
Way of simplifying binary multiplication
Is there a way to simplify multiplication of binary numbers regardless of digits? Or do we always have to resort to 10-base multiplication? As computers do multiplication, there should be ways to ...
2
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1answer
57 views
Is there a sequence of primes whose decimal representations are initial segments of each other?
I.e., is there a sequence of primes whose decimal expansions have the following form:
$$a_1,\ a_1a_2,\ a_1a_2a_3,\ a_1a_2a_3a_4, \dots$$
What about with the order of the digits reversed, so each ...
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
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1answer
35 views
using >>, -, + to make a number X times the constant K for the following numbers
if were only allowed to use >>, -, + to make a number X times the constant K
lets assume K is 17
and K is 20
how to make an expression for each
I was trying to think of ways to do this but I cant.
3
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1answer
60 views
Find the solutions of Boolean equations
It's given 4 Boolean equations. I need to find the number of solutions of each.
$a)\ x_{1}x_{2}\oplus x_{2}x_{3}\oplus\ ...\ \oplus\ x_{n-1}x_{n}=1$
$b)\ x_{1}x_{2}\vee x_{2}x_{3}\vee\ ...\ \vee\ ...
0
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1answer
136 views
Explanation of carry in carry out borrow in and borrow out for binary addition and subtraction with examples
Hi I am having a hard time understand what carry in, carry out, borrow in and borrow out mean
can anyone help me out and show me some examples thanks
1
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0answers
30 views
System of equations with binary variables
Is there any way to simplify solving system of equations, assuming that all variables are binary? All equations, however, are seen as equations with real (or, to make things simple, integer) ...
1
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1answer
80 views
Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?
Quick background: The output of a Linear Feedback Shift Register (LFSR) with $n$ taps is a binary sequence which is periodic of length dividing $2^n-1$. From a mathematical point of view, such a ...
0
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1answer
34 views
Multiplication over $F_{2^{31}-1}$ by power of $2$
I'm reading the source code of a stream cypher (zuc):
I cannot understand properly why they define the multiplication by power of 2 in this way:
...
1
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1answer
384 views
Simplifying Boolean Expression
I am asked to simply the following expression
$$F(a,b,c) = c’ab + c’b’ + aba + b’cb + abc + c’b$$
using the Boolean identities and finding $F'(a, b, c)$ using DeMorgan’s law
I have been trying for ...
2
votes
1answer
64 views
Binary notation in Magma
As a part of programming an Elliptic Curve Method with montgomery coordinates in Magma, I need to have an algorithm to convert a number from decimal notation to binary notation. Since there is no ...
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0answers
74 views
How to convert decimal fraction to binary with error rate?
I have 48.78000 (in base 10) number
How to convert this number to binary with max 0.0013 error rate in fraction part?
Classical convert
0.78x2=1.56
0.56x2=1.12
...............
But I don't know ...
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0answers
49 views
Solving ${\bf x} = \mbox{sgn}(A{\bf x} + {\bf b})$. Nash equilibrium of n-player game with binary decisions and linear utilities
Is it possible to solve the equation in the subject line numerically or in a closed form (unlikely)? Any algorithms?
Additional details:
$x_i\in\{+1,-1\}$
$a_{ii}=0$, i.e. all diagonal elements of ...
4
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1answer
95 views
A question dealing with residual codes.
I've been reading about residual codes, and have come across several statements that I am having trouble showing.
(1.) By using the residual code, one can show that a $[16, 5, 8]$ binary code ...
1
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3answers
210 views
Binary Sequences
Let $B_n$ = $\mathcal{P}(\{1, 2, \dots, n\})$.
The set $\{0,1\}^n = \{a_1, a_2, ... , a_n : a_i \in \{0,1\}\}$ is called the length of binary sequences of length $n$.
I want to verify and work on ...
3
votes
2answers
86 views
Binary Sequence Block
More of an informatics question, rather than applied mathematics -
Source - Zonal Informatics Olympiad 2011 Question Paper
Although, I've tried a few brute methods, I haven't really understood ...
1
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1answer
48 views
How can I quantify the amount of space required to store all possible 128kilobit mp3s?
Somone has suggested that
Within, say, a collection of every possible 30 second long MP3 file encoded at 128kbps, I'd probably be infringing on a few thousand copyrighted works.
128kilobits per ...
4
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1answer
152 views
How can I solve simple equations involving binary operators?
I have some simple equations like:
A = (X AND 1779038349) XOR ((X AND 3144134329) XOR 7047511487)
Where A is some constant and X is unknown (all numbers are 32 ...
1
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2answers
139 views
What are the last four digits in the binary expansion $1234^{5555} + 4321^{5555}$?
I'm having a lot of trouble figuring out this discrete math question:
What are the last four bits in the binary expansion of 1234^5555 + 4321 ^5555?
I need to ...
0
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1answer
28 views
Element in a 4 by 4 matrix mult-group over $\mathbb{F}_2$ such that it has a stabilizer subgroup of order 64
I want to show that there exists an column or row vector with four entries in $\mathbb{F}_2$ such that there are 64 4 by 4 binary matrices $M$ where $Mv =v$, ie $M$ leaves $v$ fixed. ie, the ...
3
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0answers
148 views
An Upper Bound for an $[n,k,d]$ Linear Binary Code.
I've been reading about the various upper bounds for different types of codes. Recently, I came across a statement that is similar to the Singleton Upper Bound that I am having trouble proving. The ...
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10answers
553 views
Function that sends $1,2,3,4$ to $0,1,1,0$ respectively
I already got tired trying to think of a function $f:\{1,2,3,4\}\rightarrow \{0,1,1,0\}$ in other words:
$$f(1)=0\\f(2)=1\\f(3)=1\\f(4)=0$$
Don't suggest division in integers; it will not pass for ...
1
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2answers
261 views
How to perform the addition of 2 (base 16) numbers?
for example 0101011(base 16) + 0111011 (base 16) =?
another ex: 7FE + 3AB = ?
6
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2answers
387 views
It it possible to “compress” a list of large numbers using their prime factors?
On a computer I can have integers on arbitrary size thanks to GMP, so it's represented in base 2 in memory.
I'm wondering if it's possible in theory to use less memory if I store only prime factors ...
0
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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 ...
2
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1answer
207 views
Calculating CRC code
I think I may be under a misconception. When calculating the CRC code, how many bits do you append to the original message? Is it the degree of the generator polynomial (e.g. x^3+1 you append three ...
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0answers
40 views
interpret reduced cost of all binary variables
I have prepared and run a Linear Programming model in SAS. I have some questions about the output that I can’t find answers to, and am hoping that someone can help.
My model contains the decision ...
0
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0answers
79 views
Maximum number of truths in an optimized truth table.
I have a math-related question:
I have a set of predicates that need to be evaluated. These predicates can have two kinds of operators; AND/OR. When such an expression is constructed my code builds ...
1
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1answer
183 views
Binary Logistic Regression Model Processing
Thanks for showing interest and wanting to help out.
My aim is to develop a model that - as accurately as possible - predicts how entities in a population will either cooperate or defect, as a % of ...
2
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1answer
51 views
Partitions of binary numbers into binary numbers with fixed digits?
If we are to have (two, for example) binary numbers, such that their sum is $100111010_2$, and given that the first number has 5 ones, and the second number has 3 ones, can I find the numbers that ...
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1answer
68 views
How to convert these numbers?
I am trying to understand number systems: (binary and decimal)
How can I convert the following numbers using the least amount of digits:
$(47)\text{base}-10$ to signed binary.
$(-27)\text{base}-10$ ...
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2answers
144 views
A similarity measure for binary sequences from a partition
I'm onto a problem about binary sequence similarity for which I have not found any existing solution. I want to share it and the approaches I have taken, although none of them convince me.
Consider a ...
0
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1answer
228 views
Analogy of Binary subtraction to decimal subtraction [duplicate]
Possible Duplicate:
How to do +, -, *, / with number in a base b?
Subtraction of numbers with arbitrary bases
This is a very basic question. But I come from non computer science ...
0
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3answers
97 views
Mathematical alternative to bit manipulation to set all bits to $0$ except the two most significant (highest order) set bits.
The following describes a function which I want to solve mathematically rather than resorting to binary bit manipulation is possible:
$y = f(x)$
where
$x$ is an arbitrary integer equal to or ...
5
votes
1answer
102 views
What function $f$ such that $a_1 \oplus\, \cdots\,\oplus a_n = 0$ implies $f(a_1) \oplus\, \cdots\,\oplus f(a_n) \neq 0$
For a certain algorithm, I need a function $f$ on integers such that
$a_1 \oplus a_2 \oplus \, \cdots\,\oplus a_n = 0 \implies f(a_1) \oplus f(a_2) \oplus \, \cdots\,\oplus f(a_n) \neq 0$
(where the ...
0
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2answers
138 views
Explanation of why the height of a binary tree $\theta({lg}(n))$.
From Heap Sort chapter of Introduction to algorithms :
Since a heap of n elements is based on a complete binary tree , its
height is $\theta({lg}(n))$.
I know this is correct but how can this ...
4
votes
1answer
67 views
Proving that $A_2(13,7) = 8$
It is not too difficult to find a binary code consisting of $8$ words, each $13$ bits long, keeping the distance between every pair of words at least $7$. I know it is not possible to find $9$ words ...
2
votes
1answer
108 views
Floating point binary arithmetic question
I'm doing a basic class on computer architecture and we dwell into Floating Point Arithmetic, I'm not looking for someone to solve my homework, I'm actually just going through old exams and I'm kinda ...
2
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4answers
987 views
binary representation of a real number
In Baby Rudin,I find reference to the fact that the binary representation of a real number implies the uncountablity of the set of real numbers.(page 30)But I have two questions:
Does every real ...
4
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2answers
171 views
Why does the $2$'s and $1$'s complement subtraction works?
The algorithm for $2$'s complement and $1$'s complement subtraction is tad simple:
$1.$ Find the $1$'s or $2$'s complement of the subtrahend.
$2.$ Add it with minuend.
$3.$ If there is ...
2
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2answers
189 views
Count the number of n-bit strings with an even number of zeros.
I am currently self-studying introductory combinatorics by reading Introduction to combinatorial mathematics. I am currently in the first chapter, and I have a question regarding one of the examples. ...
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0answers
101 views
1s surpassing 0s in binary strings of odd length
Let $A(k)$ be the number of distinct binary strings of length $2k+1,$ for which the number of $1$s surpasses the number of $0$s for the first time at digit number $2k +1$, i.e., in the final digit in ...
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1answer
299 views
The sum of powers of two and two's complement – is there a deeper meaning behind this?
Probably everyone has once come across the following "theorem" with corresponding "proof":
$$\sum_{n=0}^\infty 2^n = -1$$
Proof: $\sum_{n=0}^\infty q^n = 1/(1-q)$. Insert $q=2$ to get the result.
Of ...
3
votes
1answer
52 views
q-ary code/Latin squares
For any value of $q$ the largest number of elements in any q-ary code $C$ of length $4$, distance $3$ is $q^2$. How can we prove that this is attainable iff there are a pair of mutually orthogonal ...
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2answers
150 views
Period of a finite binary sequence
Let $G:N\to\{0,1\}$, and let $L$ be some period of $G$, so that $G(i+kL)=G(i)$. What's the best a good way to find the smallest period of $G$? I mean an algorithm that takes ($G$,$L$) and outputs the ...
0
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2answers
117 views
Number 1s in a binary grid
Consider a binary grid of size 4*4, each of cell can either have 0 or 1. Among all possible 2^16 arrangement how many arrangement of such grid exist in which each row and column contains even number ...
0
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1answer
84 views
first 1 in a bitmask using log2
I am trying to get the last 1 in a bitmask. More mathematically speaking, I have a number k, that can be written in its binary form as a sequence of 1 and 0. I want the "weight" or "index" of the last ...
