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

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1answer
44 views

Computing the Value of a minimax tree

I am asked to compute the value of a minimax tree, which each node labeled with its initial value. I am just unsure how to do it. I know that it is a minimax tree if: the root is a min node, the ...
0
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1answer
15 views

Writing a series of polynomial equations of certain degree from a sequence of binary bits using Magma

How do I write a series of polynomial equations of a specified degree from a sequence of binary bits using Magma. So far, I have the following code for converting a decimal sequence to binary. ...
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1answer
19 views

Probabilities of a Binary String

You generate a random $N$-bit binary string, and compute $X = \Sigma_1^N x_i$, where the $x_i$ are the $0$ and $1$ entries of the string. What is the probability that $X$ is odd, if $N$ is odd? What ...
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1answer
44 views

I'm trying to convert a number to binary. What am I doing wrong?

So I'm trying to convert a number to binary, but I keep getting the incorrect answer. If it matters I was roughly following this guide. Here is my work: $120 = 60 + 60$ $120 = 64 + 32 + 16 + 8$ ...
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1answer
77 views

the blood test riddle (number theory)

A microbiologist has been given a set of $100$ blood vials. Exact one of those $100$ vials is positive to a concrete disease X. The microbiologist desires to send only $7$ vials for analysis. He can ...
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1answer
33 views

Bitwise ops - The relationship between $a$, $b$, $a \wedge b$, $a \vee b$ and $a \oplus b$

In computer programming, the term bitwise operation is used to denote the use of boolean operators (and $\wedge$, or $\vee$, exclusive or $\oplus$) on corresponding bits of two numbers. Bits, in this ...
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1answer
156 views

Why is $2^{16}=65536$ the only power of $2$ less than $2^{31000}$ that doesn't contain the digits $1$, $2$, $4$ or $8$ in its decimal representation?

$65536$ is the only power of $2$ less than $2^{31000}$ that does not contain the digits $1$, $2$, $4$ or $8$ in its decimal representation. http://en.wikipedia.org/wiki/65536_%28number%29
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37 views

Is there an alternative encoding scheme to binary where similarity of pattern correlates with size of number?

If I compare binary for 7 111 and binary for 8 1000 there is no correlation between these two patterns that suggests that ...
-1
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1answer
50 views

Binary strings and recurrence relations [closed]

So the problem is: How many binary strings of length n contains 111? Give a recurrence relation Tn, where Tn is the number of binary strings of length n that contains 111. How could we possibly ...
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3answers
76 views

Determining if a relation is reflexive, symmetric, or transitive [closed]

Let $A = \{0,1,2,3\}$ Define a relation $T$ on $A$ as follows: $T = \{(0,1),(2,3)\}$ Is $T$ reflexive? symmetric? transitive?
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3answers
51 views

Finding the equivalence classes of a relation R

Let A = {0,1,2,3,4} and define a relation R on A as follows: R = {{0,0},{0,4},{1,1},{1,3},{2,2},{3,1},{3,3},{4,0},{4,4}}. Find the distinct equivalence classes of R. How do I solve this problem? ...
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1answer
39 views

Proving Equivalence Relations On A Set

Let X be the set of all nonempty subsets of {1,2,3}. Then X = {{1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}} Define a relation R on X as follows: for all S and T in X, SRT if, and only if, the least ...
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0answers
27 views

How to determine size and height balance of binary search tree?

I've been reading/ learning binary search trees and I've been stuck on the following question for a while now. I have the following tree, how do I determine the height and size balance of it? How do ...
0
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1answer
24 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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2answers
81 views

How to check quickly $\frac{2}{3}=.101010… $ holds?

Every $x \in [0, 1]$ can be expressed in the form $\dfrac{a_1}{2}+\dfrac{a_2}{2^2}+\dots + \dfrac{a_m}{2^m}+\dots$ , where each $a_i$ equals either $0$ or $1$. For such $x$, we have the binary ...
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2answers
78 views

Recursively defining sets of strings discrete math

So here are the two problems: Recursively define the set of bit strings K that do not have 00 as its substring. How many bit strings of length 10 are included in the above set K? Can someone ...
1
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1answer
27 views

Essential Prime Implicants and Minterm Expressions

I have an exam for a university course shortly, and upon reviewing one of my assignments I have come to realize that I don't understand why I have lost marks/how to do a couple of questions. Hopefully ...
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3answers
28 views

Binary remainder not equal to the decimal remainder

I am having a weird result. I am dividing the binary number $10101010100000$ by $10011$. In binary division. I get $R= 0100$ which is 4. However, If I consider the decimal representation of the ...
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1answer
31 views

Binary Representation of the Collatz Conjecture

What is the benefit of looking at the binary representation of the collatz conjecture. I know that it makes the computation easier because there is really one operation involved which is multiplying ...
0
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1answer
25 views

why borrow two 1s in binary substruction?

In binary subtraction i have seen some tutorial and some sites that during 0-1 process borrow value from next 1s. Let's say one of tutorial is this ...
2
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1answer
46 views

What is the minimum longest repeated substring of a binary string of size n?

The longest repeated substring of 0111011 is 011 for example. My question is given the size of a binary string, what is the shortest this longest repeated substring can be. I have computed values for ...
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1answer
31 views

Evaluating the decimal equivalent of binary numbers in; sign and magnitude, one's complement and two's complement

For example, i have this binary number : 1011 1101 Now i wish to evaluate the decimal equilant using sign and magnitude, one's complement and two's complement. Now for sign and magnitude, i know the ...
2
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2answers
190 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 ...
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1answer
17 views

Why Are The First and Last Entries of a Binary Reflected Gray Code Sequence Adjacent?

Some Information on Gray Codes If you're rusty or unfamiliar with Binary Reflected Gray Code, but want to try and help, here is a youtube tutorial explaining what they are: ...
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0answers
47 views

binary search worst case for a set database of entries some good some bad

A database has 10,000 sorted entries, 20% known to be good. When looking up a record in the database, the good entries account for 60%. Two design options are considered to store the data in the ...
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2answers
8k 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 ...
3
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1answer
61 views

Proofs involving some general formulae for trees and binary trees.

So here I have 3 tree-related questions. 1) Let $n\geq2$ and let $d_1 ≤d_2 ≤···≤d_n$ be a sequence of integers. Show that there is a tree with degree sequence $d_1,d_2,...,d_n \Leftrightarrow \sum ...
4
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1answer
107 views

Disjoint subsets and Number of 1's in the binary representation

For a subset $S$ of $[n]$, let $\chi(S)$ denote the $n$ bit 'characterisitc vector' of $S$, i.e., $\chi(S)=(a_1, a_2, \ldots, a_n)$ where $a_i=1$ if $i \in S$ and $a_i=0 $ if $i \notin S$. Think of ...
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4answers
7k 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 = ~ ??? $
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1answer
800 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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2answers
33 views

Base-n arithmetic and multi-dimensional matrices

Interesting thing about binary numbers is to find their decimal value you can represent them as a multidimensional array, where each cell is indexed, starting from 0. For simplicity, let's start with ...
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0answers
18 views

Find minimum algorithm complexity

So, I have this task: Let us have square matrix $A \ size\ n\ \times\ n$ for which is true: $$A(k,l)<=A(m,p)\ if \ k <=m, l<=p$$ I need to find algorithm, which finds value X in such matrix, ...
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0answers
95 views

Looking for a best binary division tutorial

All I can found is such confusing "tutorials" like the below examples.. Even if i search it on Youtube, most videos are having dislikes and with short or unclear explanation. Is it a really hard ...
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0answers
28 views

How Leibniz invented the Binary System?

Do you know which reasoning and observations made Leibniz invent the Binary system ? Some say that he was inspired by Chinese mathematicians do we have any record of how he came with this idea ?
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3answers
102 views

Convert from binary to quinary

How to convert a number from binary to quinary system without using decimal system ? It is possible ? I want to write a program who does it.
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2answers
354 views

Sum of series with binary parity in the numerator

I'm now stuck with this question, and I don't even know where to start: Find sum of series$$\sum_1^\infty \frac{f(n)}{n(n+1)}$$, where f(n) - number of ones in binary representation of n. I wish I ...
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2answers
311 views

Convert decimal to Binary Floating Point - 8 Bit [closed]

I am trying to convert +3.5 to binary floating point, but im struggling to find the exponent. (8 Bit) Where 1st bit is the Sign, 3 bits for Exponent and 4 bits for Mantissa. Hope somebody can explain ...
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0answers
20 views

Determining whether two trees are isomorphic

Is there a (probably recursive) algorithm that can be used to determine whether two not necessarily binary ordered (sub)trees are isomorphic or not?
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1answer
381 views

Probability of a binary communication system

A binary communication system is used to send one of two messages: message A is a sequence of 0s with probability 2/3, message B is a sequence of 1s with probability 2/3, The ith received bit is ...
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3answers
45 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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0answers
18 views

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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0answers
17 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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0answers
24 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
28 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
35 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
10 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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0answers
39 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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3answers
31 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
36 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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1answer
52 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. ...