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

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Distribution of binary sequences?

I have two binary sequence and wanted to test if there is a similar patterns between the two. This is a completely new topic for me. Are there ways to define distribution of a binary sequence ...
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3answers
18 views

modulus to find 10-bit samples in 8-bit memory

For one of my electronics projects I am using an EEPROM chip that holds up to 512k bits of information, arranged in 8-bit (1 Byte) address registers. Multiply 512 x 1024 and divide by 8 and you'll get ...
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12 views

why use Unpacked BCD

I wonder why someone should ever use unpacked BCD, as packed BCD is a lot more compact, and you can also form each number. Is there a good reason to use it or not?
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22 views

What are the possible relations?

If there are two sets A and B. Set A has two elements so does Set B. How many different possible relations can we have from A to B. For example. Set A has (David, Max) and Set B has (x,y). Would the ...
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1answer
20 views

Why is the enumeration of binary strings misaligned?

If you enumerate the set of binary strings in ascending order, you get: ...
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0answers
11 views

equivalence of binary matrices in GF(2)

I have a binary matrix [G] of size 13x20. After column exchanges i obtained [G1]=[I : P]. G1 is an augumented matrix. I is an identity matrix of 13x13 and [P] is of size 13x7. Now my question is that ...
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28 views

Performing arithmetical operations (with binary numbers) using propositional logic

Clarifying some terms. By arithmetical operations I mean the four basic operations of addition, subtraction, multiplication and division. By binary numbers I mean numbers in the binary system. By ...
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1answer
8 views

haw to find the values of binary numbers in octal?

what is the value of 101111.0111 of base 2 (binary) in octal(base 8) we know that in order to translate from binary to octal we need to group the bits in groups of three and the value is going to be ...
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3answers
26 views

Binary subtraction A0 - E4

I have two numbers. The negative one is translated using 2's complement. $$ a = 160_{10} = A0_{16} = 1010 0000_{2} \\ b = -28_{10} = E4_{16} = 1110 0100_{2} $$ And I have to perform the following ...
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1answer
33 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 ...
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31 views

What are the possible dimensions of a binary cyclic code of length 37?

What about the possible dimensions of a 16-ary cyclic code of length 37? [Edit]: The cyclic codes of length $37$ are in a bijective correspondence with factors of $x^{37}-1$. Furthermore, the ...
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1answer
49 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. ...
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2answers
37 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 ...
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1answer
49 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 ...
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1answer
34 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 ...
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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 ...
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1answer
21 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 ...
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2answers
65 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 ...
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1answer
41 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: ...
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0answers
24 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? ...
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1answer
31 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 ...
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1answer
85 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: ...
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0answers
42 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 ...
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0answers
40 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 ...
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1answer
178 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 ...
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3answers
72 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 ...
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1answer
40 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 ...
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0answers
19 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 ...
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1answer
72 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 ...
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1answer
65 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. ...
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2answers
41 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 ...
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2answers
47 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, ...
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0answers
37 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, ...
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2answers
29 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 ...
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2answers
31 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 ...
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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 ...
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1answer
27 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 ...
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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 ...
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1answer
18 views

Algorithm for Converting Non-balanced Base-n to Balanced Base-n (for odd n)

Let $n \in 2 \mathbb{N} - 1$. I was wondering what sort of algorithms there are for converting (non-balanced) base-n to balanced base-n, where "balanced" is as is described in this article: ...
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1answer
44 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
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1answer
19 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) ...
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2answers
98 views

How to find Bitwise AND of all numbers for a given range?

How can I find Bitwise AND of all numbers for a given range say from A to B, including both? I found a beautiful answer for finding XOR for such range. http://stackoverflow.com/a/10670524/2046703How ...
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2answers
36 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 ...
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4answers
997 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 ...
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2answers
47 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 ...
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1answer
42 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 ...
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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 ...
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1answer
31 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 ...
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3answers
25 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 ...
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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 ...