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

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2answers
73 views

Is it possible to not have irrational numbers?

(Math noob question): Is there a base that can be used like binary that produces no irrational numbers or numbers with an infinite amount of one number after the decimal (don't know the name)? I feel ...
2
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1answer
38 views

Getting the nth bit of a decimal number

I have a formula for decoding a 3-bit data object: $$T = 68 + 2 \sum_{i=0}^22^iTempA_i$$ where $TempA$ is the 3-bit object and $TempA_i$ is the $i$'th bit from the right. I am trying to rewrite this ...
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1answer
31 views

Where can I find a binary calculator that can do exponentiations, roots and logarithms?

I've searched on Google, but all I found was binary calculators that can do additions, subtractions, multiplications and divisions, nothing else.
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1answer
24 views

Express a binary operation in decimal

Is there a way to represent binary operation in decimal. What I mean with this is for example a set of decimal operators that would give the same result as a x>>n a ror(x), etc. So far the only thing ...
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1answer
117 views

Prove through structural induction that a binary tree has an odd number of nodes

A full binary tree is a binary tree where every node has either 0 or 2 children. Prove that every non-empty full binary tree has an odd number of nodes. I dont know how to get started with this ...
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0answers
13 views

Estimating how many searches will be needed to justify time spent on presorting an array.

Problem Estimate how many searches will be needed to justify time spent on presorting an array of $10^3$ elements if sorting is done by merge sort and searching is done by binary search. (You may ...
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1answer
14 views

If gen matrix has even weigth rows, do codewords have even weigth for non binary code?

Is that true that in a non binary code C every codeword has even weight if and only if every row of G has even weight?
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2answers
28 views

Trying to understand binary number equation

I'm reading a book called "The Elements of Computing Systems" by Noam Nisan/Shimon Schoken. There's an excerpt which includes some math that I'm struggling to understand (limited math background; I ...
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0answers
40 views

Proof by Induction for Splay Tree?

I'm preparing for an exam about Trees. One of the questions that appear in Mark Allen Weiss' "Data Structures and Algorithms Analysis in C++" is: Prove by induction that if all nodes in a splay tree ...
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2answers
52 views

Equivalence relations for $\mathbb{N} \times \mathbb{N}$ question

On the set $\mathbb{N} \times \mathbb{N}$ define $(m, n) \sim (k, l)$ if $m + l = n + k$. Show that $\sim$ is an equivalence relation on $\mathbb{N} \times \mathbb{N}$. Draw a sketch of $\mathbb{N} ...
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0answers
83 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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1answer
22 views

Does decimal fraction has hex value?/can hex be fraction?

I was wondering if a decimal fraction could be converted into a hexadecimal fraction? I have seen it many times ? but I have been also told that decimal or binary fraction has no meaning in hex. ...
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1answer
45 views

How many binary string are there such that there are no k consecutive characters are the same?

Given number $n$ and $k$. Count the number of string with length $n$ such that there are no $k$ consecutive characters are the same. Example with $n = 3, k = 3$, the answer is $6$. ($110, 001, 101, ...
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1answer
26 views

Why do we add 6 in BDC addition.

When performing addition to BCD, if we get an invalid BCD, we remedy this by adding a binary $6$ to our sum. Example: $0101 + 0110 = 1011$ (Invalid in BCD) So, we add $6$ to fix this. $1011 + 0110 ...
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2answers
30 views

Why are these two conversion methods (base 10 to base 2) equivalent

I've come across two methods for converting a base 10 number into its base 2 equivalent. I want to know why they are equivalent. Method 1: We're given a number $N$ to convert into binary 1) Find the ...
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1answer
25 views

Can we transform given strings to get the same string?

There are 2 binaries string $A, B$ (string just contains $0$ or $1$) Input: $A_1, A_2,\dots,A_{50}$ and $B_1, B_2,\dots,B_{50}$ Note that: $A_{51} = B_{51} = A_{52} = B_{52} = \dots = A_{\inf} = ...
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1answer
19 views

Boolean Algebra - What is the meaning of f(x) = ∑(N)?

Suppose you had: f(x,y,z) = ∑(2,3,4,5) What does this represent or map? For each of the variables x,y,z?
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0answers
21 views

Converting From Different Number Systems

I've been taught to convert from base 2 to base 10 using the following process: 10110 = $0\times1 + 1\times2 + 1\times4 + 0\times8 + 1\times16 = 0\times2^0 + 1\times2^1 + 1\times2^2 + 0\times2^3 + ...
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1answer
39 views

Number of 2n-digit binary sequences

Find the number of 2n-digit binary sequences in which the number of 0's in the first n digits is equal to the number of 1's in the last n digits. I'm not sure how to approach the question. My ...
0
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1answer
31 views

From an expression raised in a power of 2 to an expression raised in the power or 10

Is there a simple/"easy" way to convert a big number from a power of $2$ to a power of $10$ equivalent. Example: I had $2^{127}\cdot 1.9999999$ which I did the multiplication got the result and from ...
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2answers
50 views

Determine whether a number has an even number of 1's or not in a binary base

Assume that I have an ordinary number in Decmical base, now what I want to know is determining whether it has an even number of 1's in a binary base or not.and yet again I should emphasize the fact ...
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2answers
32 views

Binary solving problem. 50 in binary number

The asnwers doesnt make sence for me. The binary number of 50 is 110010. Do I overlook something?
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1answer
17 views

Linearly independent rows in a binay matrix

I need the algorithm to finding only the linearly independent rows in a binary matrix using XOR function. Example 1: The result: Example 2: The result: R4 is not included because:
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3answers
3k views

Why are huge binary numbers about 3.3218 times longer than their decimal counterpart?

Why are huge binary nubers about $3.3218$ times longer than their decimal counterpart? I thought about this when I was writing this Python code: ...
0
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1answer
61 views

Is there a binary [10,6,4] code?

Using the sphere padding packing bound formula I can conclude that 1 + 12 + 66 $\ge$ $2^{6}$ which indicates that there MAY be a binary [10,6,4] code, however I cannot prove that there is. How can I ...
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1answer
51 views

Finding a standard generator matrix given a binary code

My question is how do I find the standard generator matrix of a binary [7,6,2] code? From what I understand a generator matrix for $C$ is any $ k \times n$ matrix $ G$ with entries in $ ...
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1answer
60 views

Binary Gaussian Elimination of a matrix

Can anyone help me find the algorithm for the Binary Gaussian elimination of a matrix. for example: The output:
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1answer
5 views

How can I determine the base of the following numbers for the operations to be correct?

Given: 24)A + 17)A = 40)A How can I find the base of the following number (A) so the operations are correct? NOTE: I am not sure what topic this would fall under. Hence sorry for any misplaced ...
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3answers
991 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. ...
1
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2answers
25 views

Prove that the binary representation of a number n will use floor(lg(n)) + 1 bits.

I'm taking Computer Algorithms class and one of my problems is from Skiena's Algorithm Design Manual, 2-41: Prove that the binary representation of $n \ge 1$ has $\lfloor \lg n \rfloor +1$ bits ...
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3answers
95 views

How many bits are needed to represent the integers 3^1000 and 2^1000?

I'm struggling with a math exercise here, and I would gladly appreciate some help. My problem is that I've encoutered some very big numbers such as $3^{1000}$ and $2^{1000}$ and I want to estimate ...
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0answers
39 views

Leibniz Binary Representation of Squares

Leibniz claims to have found patterns in the square numbers and their binary representations. I cannot see any patterns at all. Here are the first ten squares and their binary representations, can ...
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0answers
12 views

Redundant Binary Representation

Is it possible to have a technique using Redundant Binary Representation so that repeated addition can be obtained with no carry propagation time?
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2answers
26 views

One output for input of $n$-tuples using AND, OR, NOT

Let $B$ be set of $\{0,1\}$ and $B_n$ be the set of all strings of length $n$. How many functions can be constructed from $B_n$ to $B$ using logical operators like AND, OR, NOT. Help $\rightarrow$ ...
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0answers
89 views

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 ...
2
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1answer
116 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
46 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 ...
2
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2answers
57 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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0answers
20 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
42 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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1answer
54 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
103 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
41 views

Turn recursive definition of a function into its close form

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
49 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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1answer
65 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
52 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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3answers
51 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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4answers
338 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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0answers
51 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 ...
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1answer
22 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 ...