Questions related with (base 2) representation of numbers and their unique properties arising out of number representation.

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2
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1answer
107 views

Random infinite binary sequence

What I mean by random infinite binary sequence is an infinite sequence of $0$'s and $1$'s with probability of occurrence in this sequence equal to $1/2$ (all digits being equally likely). How is it ...
0
votes
3answers
344 views

Binary Programming with nonlinear constraints

i have the following type of problem i'm interested to solve: Minimize the objective function: $f(x_1,\ldots, x_8) = \sum_{i=1}^8 a_i x_i$ with $a_i \in [0, \infty)$ and $x_i \in \{0,1\}$ and given ...
0
votes
3answers
2k views

Comparing two 2-bit binary numbers

In order to compare two 2-bit numbers, I need to create a truth table, develop the equation for the equal more or less case, optimize the equations the the Karnaugh maps, and then develop the ...
0
votes
0answers
48 views

Binary String as number

For 1 ≤ i ≤ n− m, m < n, Interpreting the strings as binary numbers, we have that A[(i+ 1) ..(i+ m)] = 2 A[i..(i+ m− 1)] − (2^m−1)A[i]+ A[i+ m]. Can someone ...
5
votes
2answers
244 views

Nim addition- binary addition without carrying

A nim addition table is essentially created by putting, in any cell, the smallest number not to the left of the cell and not above that cell in its column. However, I know for a fact that nim addition ...
2
votes
1answer
120 views

Proof about infinite sum

Define recursively-defined function $f_x:N\to\{{0,1\}}^N$ where x belongs to [0,1): For $n=1$,$f_x(1)=0$ if $x$ belongs to $[0,1/2)$, $a_1=0$, $b_1=1/2$ in this case; $f_x(1)=1$ if $x$ belongs to ...
1
vote
1answer
41 views

Multiples of $5$ in base $2$

As a follow-up question, what can be said about multiples of $5$ in base 2? I think I must look at the last two digits, but I am not sure what the whole idea might be.
1
vote
1answer
88 views

Even numbers in base 2

We all know even numbers are the ones that end in even digits. How do we analyze even numbers in base 2?
-4
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2answers
3k views

Binary Subtraction of Two Unsigned Integers

For unsigned integers $ X = 00110101 $ and $ Y = 10110101 $, determine the following values: $ X + Y = (\text{My answer is}) ~ 11101010 $. $ X - Y = ~ ??? $ $ Y - X = ~ ??? $
-3
votes
3answers
889 views

Need help converting a number into IEEE floating point format

I need to convert the number $74 \frac{5}{14}$ into IEEE floating point format. Can someone help me with this
2
votes
2answers
93 views

Twos complement notation question?

I have a quick question how do you do the two complement system, For example say I have in two complement a $6$ which is $0110$ and $3$ which is $0011$ and I want to add $6+(-3)$ I know what five is ...
2
votes
1answer
825 views

How do you work with the IEEE 754 32-bit floating point format?

I'm having trouble completing a question that deals with the IEEE 754 32-bit floating point format, primarily because I don't know how to use it. I was hoping someone here could clarify for me using ...
14
votes
8answers
2k views

Fractions in binary?

How would you write a fraction in binary numbers; for example, $1/4$, which is $.25$? I know how to write binary of whole numbers such as 6, being $110$, but how would one write fractions?
2
votes
1answer
346 views

Finding the binary representation of the $n$th Fibonacci term

Objective: To find the binary representation ( or no. of 1's in binary representation) of nth term in Fibonacci sequence where n is of the order 10^6. My current approach: Find nth term (in decimal) ...
-1
votes
1answer
345 views

Multiply two large numbers in under 1000 instructions using reduced ISA with only 7 registers [closed]

Is it possible to multiply two large (15 bit) numbers efficiently (in under 1000 instructions) using the following ISA: ...
1
vote
1answer
284 views

Arrangement of binary bits

I have $n$ numbers of bits. $\frac{n}{2}$ of those bits must be $1$ and $\frac{n}{2}$ of those bits must be $0$ (meaning $00001111$ or $10101001$). How many different binary numbers can I make? Is ...
3
votes
2answers
8k views

How can I convert 2's complement to decimal?

Suppose I have the 2's complement, negative number 1111 1111 1011 0101 (0xFFBB5). How can I represent this as a decimal number in base 10?
0
votes
1answer
370 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 ...
1
vote
2answers
2k views

Represent the following decimal values in 8-bit 2's complement and hexadecimal

-27: 11100101 -128: 10000000 I'm having trouble coming up with the hexadecimal representation. Does it change if my numbers are represented in 2's complement as opposed to just regular binary? ...
1
vote
1answer
137 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
vote
1answer
188 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
votes
2answers
238 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
vote
3answers
1k 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
votes
1answer
79 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
vote
1answer
38 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
votes
1answer
70 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
votes
1answer
2k 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
45 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
vote
1answer
137 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
votes
1answer
43 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
vote
1answer
478 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
194 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 ...
4
votes
1answer
242 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
vote
3answers
337 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
145 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
vote
1answer
61 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
votes
1answer
723 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
vote
1answer
208 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
votes
1answer
35 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
votes
0answers
203 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 ...
5
votes
10answers
588 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
vote
2answers
1k views

How to perform the addition of 2 (base 16) numbers?

for example 0101011(base 16) + 0111011 (base 16) =? another ex: 7FE + 3AB = ?
7
votes
2answers
1k 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 ...
2
votes
1answer
453 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 ...
1
vote
0answers
79 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
votes
0answers
130 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 ...
2
votes
2answers
443 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
votes
1answer
88 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 ...
1
vote
1answer
75 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. $(-27)\text{base}-10$ ...
1
vote
2answers
192 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 ...