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

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Proving that number of codes with even weight is the same as number of codes with odd weight for a specific code book

Consider the $[n,n]$ code-book $C_0=\{0,1\}^n$ with $n$ being odd and the codes $c_i \in C_0=[c_1,c_2,...,c_{2^n}]$ being sorted in the ascending order of hamming weight (from $0$ to $n$). Now let's ...
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1answer
33 views

Computing $ 001001_2 - 110101_2$ (base $2$), and representing the result in signed magnitude format

I've been asked (for homework) to do $ 001001_2 - 110101_2$ (base 2) and to represent the answer in a signed magnitude format. EDIT: I'm specifically asked: Perform subtraction on the given ...
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1answer
37 views

Converting 16bit float to Base10 and vice versa

Hi! I have some difficulties understanding how I'm supposed to calculate this 16bit float to base10. This is something that is coming up on a test so I would be pleased to learn how this is supposed ...
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2answers
44 views

Linear Code (9,5): Is my Parity Check correct?

I have an exercise about designing parity checks for the Hamming (9,5) group code with minimum distance $3$. I use the following notation for the generator matrix: $$ ...
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2answers
263 views

Quick logarithm calculation

In coming up with an algorithm for finding log (10) base 2, these are my thoughts. I wanted to know if this makes sense and how could I truly make it more efficient. The requirements are strictly not ...
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0answers
10 views

similarities between two binary matrices

I want to measure the similarities between two matrices A and B. Both A and B contains the feature vectors of sounds and are in binary format. i want to see what is the similarities between these two ...
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1answer
26 views

Set of points of $[0,1)$ that have a unique binary expansion

Let $Y$ denote the set of points of $[0,1)$ that have a unique binary expansion. Then $Y$ has a countable complement so $m(Y)=1$, where $m$ is the Lebesgue measure. I have to confess that I do ...
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correlation coefficient between ordinal and binary variables spss or stata [closed]

First of all, I know only the basics regarding correlation. I have two variables, the one is binary (Yes/No) and the other is likert scale (1=not at all, 2, 3, 4, 5=very much). I want to find the ...
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1answer
26 views

How to understand the perfect binary tree formula?

I got this paragraph by reading "python algorithm", in which it mentioned `some knights participate in an knockout match, how many mathes do they need to produce the winner. It's answer says: I'm ...
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1answer
32 views

Distance measures for binary data

I was wondering what are some good distance measures for binary data that have the following properties. I know that there are measures like the Jaccard index and the Dice Index, but they don't ...
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1answer
33 views

Absolute and relative error of a binary number?

Given is the following system $A:={ \pm 1.a_1 a_2 a_3 a_4 \cdot 2^e}$, $a_{i}\in \left \{ 0,1 \right \}$, $i\in \left \{ 1,2,3,4 \right \}$, $e\in \left \{ -8,\ldots,8 \right \}$. Find the absolute ...
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1answer
41 views

Mutiply Hexadecimal

I'm looking for a effective way to multiply Hexadecimal For instance, i have to find value of the quadruple of 0.FEDC 0.FEDC * 4 = ??? Normally, i will have to change the hex to binary : ...
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1answer
463 views

Arithmetic Overflow and Underflowing

I am a bit unclear about underflowing in terms of binary representation. Let's say that an unsigned 8-bit variable gets overflown from the addition of $150+150$. A signed 8-bit variable gets ...
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1answer
30 views

Turn recursive definition of a function into direct formula

I'm creating a tree diagram, and I'm trying to calculate the amount of white spaces I need at the left side. As you can already see this is done in a program. The formula goes like this: $$ ...
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1answer
46 views

How to minimize the square of $\sum b_i x_i$ where each $b_i$ can be either $0$ or $1$?

Would you please help me solve the following problem where $b_{ij}$ is my decision variable that must be determined and all other parameters are known. $$\min \left(\sum_{i=1}^n b_i x_i\right)^2$$ ...
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3answers
45 views

How to square a number in binary system?

If I want to find the square of 111 (written in binary) what do I do? I'm confused and keep on hearing different answers.
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1answer
31 views

Having problem with 10's complement subtraction

From what I've found, to find A - B using 10's complement; where A and B are decimals Let A = 215 , B = 155 Find 10's complement of B = (1000 - 155) = 845 Add 10’s complement of B to A If it ...
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1answer
27 views

Notation for show that a variable is binary?

Are there a "math letter" that represent the set of binary variable $\{0,1\}$? Like, when writing e.g., $a \in \mathbb{R}$, we know $a$ is real. I only know this notation $a \in \{0,1\}$, but is this ...
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1answer
34 views

Cubing a Minterm

I've just been going over some stuff I should actually already know - and I've come to a question that has really stumped me, (my math skill are lacking) and I don't actually know where to begin on ...
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1answer
61 views

why binary is read right to left

May somebody explain this in other words? http://wiki.answers.com/Q/Why_do_you_read_binary_digits_right_to_left I know this is an akward question, but I really want to know the answer, it's just ...
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3answers
222 views

How to convert an infinite binary fraction into a decimal fraction

I am asked to write the infinite binary fraction $0.(1011)$, where the $1011$ is the repeating part, as a $\frac pq$ fraction. What are the steps to do this? EDIT: If $0.(1011)$ was in base 10, I ...
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4answers
54 views

How do I convert from binary base to decimal?

I have a homework problem and I don't understand it. Here is the problem: The base two number 11111(base 2) has the same digit in all places. The same number can be written in different bases. Find ...
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1answer
370 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) ...
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0answers
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Recurrence relation for Binary String Question

I have a question which has been a little stumped. I'm pretty sure I know the answer, but don't know how to prove it to be true. Here it is: "Given an infinite length random binary string, what is ...
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4answers
481 views

How many bitstrings of length n contain an equal number of zeros and ones?

How many bitstrings of length n contain an equal number of zeros and ones? Progress Does $n!/2$ work as a solution since we know $n$ is even? For example, 000111 rearranged, $6!/2$? What ...
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1answer
20 views

Finding the leading exponent of a binary number

Let's say that the binary representation of a number $k$ is $2^{X_n} + 2^{X_{n-1}} + \dots + 2^{X_0}$ with each term in this polynomial having a $1$ or $0$ multiplied to it (I just haven't showed them ...
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1answer
70 views

Find the pair of values $a[i]$, $a[j]$ such that $a[i]\,\&\,a[j]$ is maximum

Given a list of positive integers, find the largest possible value of $a[i]$ $\&$ $a[j]$, where $i$, $j$ are indices of the list. $ i\ne j $, $a[i]\,\&\,a[j]$ is bitwise AND of $a[i]$ and ...
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0answers
28 views

Concrete math generalized josephus recursion understanding 1.15

I am studying through the josephus problem in concrete math , Here is the equation of binary form $$f(1) = α ;$$ $$f(2n + j) = 2f(n) + β_j ,$$ $$\text{ for } j = 0, 1 \text{ and } n \geq 1$$ this ...
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1answer
21 views

Determine fraction length of fixed-point binary

How to determine fraction length of fixed-point binary so that distinct entries of a group of decimal numbers (for example: 1, 0.456, 0.444) remain distinct after converting them from decimal to ...
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2answers
17 views

Guessing Birthday Binary-Implementation Set Size

Guessing a persons birthday day-of-month, i.e. a number ranging from 1 to 31 by dividing the numbers 1 to 31 up in 5 sets. A binary number for decimal integers between 1 and 31 has at most five ...
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1answer
62 views

Count 1-bit in binary integers

Given an integer range [A,B], (1) What’s the probability to get a 1-bit if we first randomly choose a number x in the range and then randomly choose a bit from x? (2) What’s the expected number of ...
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2answers
42 views

binary and floating point representation

suppose that we have following binary digits $00011001.110 $,we can do following thing $00011001.110=1\cdot2^4+1\cdot2^3+1\cdot2^0+1\cdot2^{-1}+1\cdot2^{-2}=25.75$ then what does means? We then ...
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2answers
72 views

Half-Adder Exercise

My exercise is the following: Make a circuit which outputs X^3 of two bit input of X. Use the lowest number of HALF ADDERS as you can. I don't really understand ...
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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?
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2answers
28 views

Polynomial representation of binary

It is well known that we can represent binary using polynomial. For example, $11$ can be represented as $x+1$. So when we compute $11\times11$, we should obtain $1001$, which is equal to $9$ in ...
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1answer
336 views

Finding a rational number which is simply normal to relatively prime bases

Let $n\ge 2\in\mathbb Z$. Suppose that a base-$n$-decimal $(0.a_1a_2a_3\cdots)_n$ represents $\sum_{k=1}^{\infty}\frac{a_k}{n^k}$ where $a_{i}\in\{0,1,\cdots,n-1\}\ (i=1,2,\cdots)$ is each digit ...
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1answer
41 views

Formula providing binary numbers based on digit 1 occurences

I would like to find a formula which gives me all binary numbers which contain the digit "1" a certain number of times. For example to times as in this sequence: ...
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2answers
114 views

Combinatorics: Binary Strings

Are the these 2 binary generation expressions equal? If so, how do I simplify my answer to match the solution's? Question: The set of binary strings where the length of each block of 0s is divisible ...
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2answers
140 views

Binary Strings Question

prove that the following expression for a set of binary strings S is ambigious S = {101,1101,1011}* Thanks for all your help!
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2answers
1k views

Modulo 2 binary division (XOR not subtracting) method

I have attached an image showing a Modulo 2 binary division. I can roughly understand the working below which is using XOR calculation but I am not sure how the answer (in red) is being computed ...
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1answer
36 views

Binary string block recurrence

Let $a_n$ be the total number of blocks for all $2^n$ binary strings with length $n$. Prove the following recurrence: \begin{equation*} a_n = 2a_{n-1} + \frac{2^{n}}{2} \end{equation*} For example ...
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3answers
236 views

Number of binary strings with $n$ ones and $m$ zeros

$f(n,m)$ is the number of binary strings with up to $n$ ones and up to $m$ zeros. Prove that the number of possible strings is: $${n+m+2 \choose n+1} -1$$ I got to the point that: $$\sum_{a=0}^n ...
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1answer
21 views

How to represent a job-sequencing?, with binary code

Suposse a job sequence of 6 jobs, as 3-5-4-2-6-1, that point the job 3 is attended in 1st place, and then the job 5,.... How could I represent this sequencies with binary code to use in metaheuristic ...
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3answers
77 views

How do I add multiple binary numbers without using a partial sum?

I know how to add binary numbers but what I normally do is add the first 2 binary numbers and then add the 3rd one to their sum. It is really slow. $$ 111_2 + 111_2 + 111_2 + 111_2 $$ Here is ...
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Efficient way to compute the binomial using $(2^k+1)^{k+1}$

The following web page: "http://introcs.cs.princeton.edu/java/78crypto/" (at Exercise 28) effectively says that: "Pascal's triangle. One way to compute the $n$-th row of Pascal's triangle (for $n ...
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0answers
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Is there a way to get the n-th of bits of 2^k

I have a large number N=O(2^k). For simplicity, let's say that N=n^k. However, I only need the n-th bits of N, say for example the 10-th to 16-th bit of N... without calculating the full expansion... ...
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7k views

Subtract Binary Numbers with 1`s Complement

I'm trying to figure out how to subtract two binary numbers with a complementary one or two, When I need to address carrier and when not? Do I need to solve the problem in decimal numbers? And ...
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3answers
4k views

Binary long division for polynomials in CRC computation

I am trying to learn binary long division, and I am confused. An example in my book gives that $10011010000/1101 = 11111001$ plus a remainder of $101$, which doesn't make sense, since $1001$ is not ...
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1answer
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Relations between NIM-addition and addition

I will note $\oplus$ the NIM-addition. This is a commutative group law. To obtain $a \oplus b$, you decompose a and b in binary, and you sum like this : 0+0=0 ; 1+0=1 ; 1+1 =0 (it's the xor ...