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

learn more… | top users | synonyms

0
votes
1answer
34 views

What is a signed number?

When is the meaning of "signed number"? A signed number simply means a number that is negative, correct? Sorry if this seems like a stupid question but I'm just starting to get deep into ...
5
votes
1answer
51 views

How many numbers from $1$ to $2^n$ will have $``11"$ as substring in binary representation?

For example say, $n = 2$. So our set is $\{1, 2, 3, 4\}$ in base $10$ and $\{1, 10, 11, 100\}$ in base $2$. So Output $1$, because only one number i.e. $3$ is there such that it has $``11"$ in it. ...
0
votes
2answers
10k 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 ...
1
vote
2answers
46 views

What am I doing wrong when multiplying binary numbers together?

This is from Discrete Mathematics and its applications I was able to get sum pretty easy. I am trying to follow this example in the book to get the product of the two binary numbers Here's my ...
0
votes
1answer
208 views

Convert hexadecimal numbers to floating-point format using single-precision IEEE 754 format

I need help with converting hexadecimal numbers to floating-point format using single-precision IEEE 754 format. Hex numbers such as 312A. how do I go about converting it? I know how to convert from ...
0
votes
1answer
38 views

Converting from twos complement to decimal?

I am currently reading a textbook and I can't seem to understand what the examples in the book did. I do believe it is an error with the book, but if not can someone explain? How come there is no ...
0
votes
0answers
30 views

How to convert a decimal to a $2$'s complement [duplicate]

On this link How can I convert 2's complement to decimal? is a good description. I need to know how to convert from a negative say $-26$ to a two's complement binary and from a decimal with a decimal ...
0
votes
1answer
32 views

Simplifying Simple Boolean XOR Expression (!AB + A!B)

I am trying to simplify the 5 gate XOR from a A!B + !AB expression to a (A + B)!(A + B) implementation. How can I convert ...
0
votes
1answer
160 views

How to convert from floating point binary to decimal in half precision(16 bits)?

I'm trying to convert a 16 bit precision binary number to decimal format however I am completely failing to do so. The binary I'm trying to convert is $0101011101010000$ My current method is: ...
0
votes
2answers
71 views

Possible distinct binary tree structures at depth d

I'm trying to figure out a recursive formula for the number of possible distinct binary trees at any depth d. I haven't been able to find any sort of sources on this. basically, at depth 0, the only ...
0
votes
0answers
27 views

Binary to Decimal Floating Point Number

I seem to be having difficulties trying to figure this out: I have a Binary 0101011101010000 and I'm trying to compute the decimal floating point number, in the IEEE-754 format Can somebody help? ...
0
votes
1answer
110 views

Grade School Multiplication Algorithm for Binary Numbers explanation

I under stand the shifting but not why it will always give the right answer? For Example: ...
0
votes
1answer
36 views

Converting from Octal to Decimal.

I have the value $(3738)_8$ and I want to convert it to decimal. The answer i believe is $$(3 \times 8^3) + (7 \times 8^2)+ (3 \times 8^1) + (8 \times 8^0) = 2016$$. My question is that on some ...
1
vote
0answers
49 views

Generating function from a set of binary strings

So this question is in my textbook and there's no solution, so I'm seeing if I can get a confirmation? Q: Let $S$ be the set of all binary strings of length 4, where for each string $a\in S$, the ...
7
votes
1answer
209 views

$N$ perfect logicians wearing hats

I once came across the following riddle: (assume $N$ to be extremely large) There are $N$ perfect logicians arranged in a vertical row. They are allowed to strategize before the game, during the ...
1
vote
0answers
41 views

Has anyone established an upper bound for the least integer $k$ such that infinitely many primes have at most $k$ ones in their binary representation?

Has anyone established an upper bound for the least integer $k$ such that infinitely many primes have at most $k$ ones in their binary representation? $2$ is the only prime with $1$ one, the Fermat ...
1
vote
3answers
83 views

Defining a bijection with binary strings

Let $n\in\mathbb N$. Then a binary string of length $n$ has the form $a_1a_2...a_n$ such that each $a_i$ is either 0 or 1. Define $E_n$ to be the set of all binary strings of length $n$ with even ...
0
votes
1answer
42 views

Understanding binary combinatorial problem

It has been quite some time since I've done permutations and combinations, and I'm attempting to remember the proper way to go about solving this issue (not a homework assignment, more of a thought ...
0
votes
1answer
67 views

Using XOR operation repeatedly

There are $n$ binary digits, from $A_0$ to $A_{n-1}$. Each operation consists of the following 2 steps: Each digit is replaced by the XOR addition of itself with the next digit. ...
2
votes
2answers
57 views

Mathematical Relations in Computing - Unary

I have this question that's bugging my mind: "Discuss by giving suitable examples the role of mathematical relations (Unary, binary and ternary) in computing." I'm sure it's a very simple question, ...
0
votes
0answers
21 views

Binary Overflow Detection

I am trying to solve several problems, which are binary and encoded using the 2's complement system. One problem has stuck out to me: 0111 + 0001 Both are positive, with 0111 being 1+2+4 or 7, and ...
0
votes
1answer
76 views

Find number between $A$ and $B$ with maximum set bits?

Given two integers $A,B$. Find number $N$ which has maximum number of set bits in its binary form and lies between $A$ and $B$ inclusive. Is there any approach for this question. Also if there are ...
1
vote
2answers
64 views

Converting Decimal to Hexadecimal

MathExchange, I am trying to learn more about computers, and one thing I have opted to teach myself is decimal to binary, and decimal to hex conversion. From the web, I have found tutorials on ...
2
votes
0answers
49 views

An expression for the number of n-bit binary strings with at most k ones (without summations)

Say we need to find an expression for the number of binary strings of length $n$, which have at most $k$ ones. My solution was to split the problem into $k+1$ cases, where the number of ones, ...
1
vote
2answers
33 views

Correlation between Binary and N-dimensional simplexes

I found an interesting correlation between binary numbers and $n$-dimensional simplexes and I'm trying to find where I can find more information on the subject. I noticed that binary representations ...
1
vote
2answers
32 views

How many numbers with given amount of ones in their binary form?

I was practicing for a programming competition and I got the following problem, which I was unable to solve: It is given a number N. Find the amount of x, y values, where x > N, y < N and the ...
1
vote
1answer
72 views

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 ...
12
votes
4answers
1k views

Is Cantor's diagonal argument dependent on the base used?

Applying Cantor's diagonal argument to irrational numbers represented in binary, one and only one irrational number can be generated that is not on the list. Wikipedia image: But if you change ...
19
votes
3answers
1k views

What do bitwise operators look like in 3d?

The hypothetical relation is $z = \mathrm{xor}\left(x,y\right)$ where xor is any bitwise operator such as AND, OR, NAND, etc. I see that these operations may be defined for integers trivially using ...
1
vote
1answer
30 views

Binary Multiplication Counting Ones

Excuse my formatting. I have noticed the following but know no way to prove it. Given the multiplication $y=(2^n-1)\cdot m$, where n,m are positive integers and $m\leq(2^n-1)$. Prove that the count ...
1
vote
1answer
45 views

Are some infinite fractions in one counting system non-infinite in another?

I'm curious whether some infinite periodic fractions in one counting system (e.g. decimal - 10/3 = 3.33333...) turn out to be non-infinite in another system and vice - versa. Please excuse me if my ...
4
votes
3answers
286 views

An odd question about induction.

Given $n$ $0$'s and $n$ $1$'s distributed in any manner whatsoever around a circle, show, using induction on $n$, that it is possible to start at some number and proceed clockwise around the circle to ...
4
votes
1answer
45 views

Least squares with matrix in $GF(2)$?

Here's an example of a problem I'm working on involving finding combination of bit vectors that yield a certain sum (in the $GF(2)$ sense): $ \begin{pmatrix} 1 & 1 & 1 & 1 & 0 & 0 ...
2
votes
1answer
25 views

float vector to binary integer vector transformation preserving dot product

Is there a transformation of a set of float vectors to a set of binary integer vectors that preserves the dot product. I found conformal transformations but I'm interested in large vectors (size 300) ...
3
votes
2answers
38 views

Classification of numbers on the base of binary representation

The problem is the following. I would like to find a simple algorithm or principle of classification of numbers regarding their presentation in binary form. Let's consider an example. The numbers by ...
0
votes
1answer
50 views

Unfair coin probability (P) that results in 0.5% chance of getting x tails out of y tosses?

For an unfair coin toss that produces heads with probability P, what is the value of P that will result in 0.5% (i.e. 0.005) chance of getting exactly x tails out of y tosses? i.e. is there a general ...
0
votes
2answers
52 views

distribution probability question involving binary functions for certain n<2^10

For any positive integer n, let G(n) be the number of pairs of adjacent bits in the binary representation of n which are different. For example, G(10)=3 because the bits of $1010_2$ change at all ...
1
vote
0answers
79 views

Probability of getting a Column full rank binary matrix

Suppose I have a $m \times n$ ($m>>n$) zero matrix (all of the elements are $0$). I want to flip $k$ ($k \ge n$ and can be controlled by the user) elements of the matrix randomly. After this ...
0
votes
0answers
33 views

How to prove that all powers of two minus one have only 1's when in binary representation?

It just came to my mind that all powers of two, when represented in binary format, are composed of only 1's, not 0's. I can see some logic behind it, however I can't seem to come up with an actual ...
0
votes
1answer
36 views

XOR function over binary vectors

I didn't really know how to name this question, it has been bothering me for some time: You are given n binary vectors of dimension $d: x_1,\cdots,x_n$; $x_i = x_{i_1},\cdots,x_{i_d}$. You are also ...
0
votes
1answer
20 views

how binary quantile regression divides the dependent variable into quantiles

I am not very clear with binary quantile regression. As if it was ordinary quantile regression, it would divide the dependent variable's value by its ascending value into quantiles. But I cannot ...
2
votes
3answers
28 views

4-bit number to decimal number

Juts like the title says: a code to convert a 4-bit number into a decimal equivalent number without using any fucntion from octave's library. Not a clue! We consider the input a binary number ...
1
vote
6answers
88 views

What is 6.5 in binary? [duplicate]

I just stumbled across a problem I never actually thought about before: decimals in binary. Can someone explain how to do it? Thanks! Note: If possible, I'd like the answer in decimals not fractions, ...
8
votes
3answers
4k views

Convert the following hexadecimal representation of 2’s complement binary numbers to decimal numbers.

I need to convert the following hexadecimal representation of 2’s complement binary numbers to decimal numbers I am unsure if I am doing it correctly or am I missing a step? a. xF0 b. x7FF c. ...
0
votes
0answers
57 views

Is there a name for this constant? (0.0100011011…)

It's the simplest number I could think of that contains any finite binary code in its digits: $$\begin{align} c &= 0.0100011011000001010011100101110111...\\ &= ...
0
votes
3answers
94 views

Isn't this the most compact binary representation of all numbers?

Here is the transformation: $$\begin{align*} &1\to(0)\\ &2\to(1)\\ &3\to(10)\\ &4\to((1))\\ &5\to(100)\\ &6\to(11)\\ &7\to(1000)\\ &8\to((10))\\ &9\to((1)0)\\ ...
0
votes
0answers
26 views

Give the idempotent generators of the four binary QR codes C1 , C2 , C3 , C4 , of length 7.

I'm having trouble on some homework. This is the last problem and I can't figure it out. Can anyone help or point me in the right direction? Thanks! For each code Ci , 1 ≤ i ≤ 4, from part (a), give ...
0
votes
1answer
143 views

Proving properties of binary relations

Attempting to find answers to solve these questions. I've been looking all over the web for references since my textbooks aren't being helpful. Now, I'm still at the starting point. ...
0
votes
1answer
51 views

how to find the binary expansion of any number in the unit interval [0,1]

For each integer $n\geq 1$ and $x\in [0,1]$, define $f_n(x)=x_n$ where $x_n$ is the $n$th binary digit of x. If x is a number with two binary expansions, use the expansion that ends with infinitely ...
2
votes
1answer
217 views

Counting binary strings that have atmost k consecutive 0's

I know how to count how many binary strings with length n and having exactly k 0's are there but i am not able to find a way to count the number of binary strings that have exactly x 0's and y 1's and ...