# Tagged Questions

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

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### Number of ways to express a binary number in a certain way

So I'm working on a problem where I get to a point where I have to count the number of solutions to an equation or at least find a decent upper bound to be used in an estimate I need later. The ...
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### How draw a sample of distant points from a set of binary numbers

I am working on a computer program where I need to sample a set of say $k$ elements from a set of binary numbers ranging from $0$ to $2^n-1$, for some integer $n$. For various reasons, I want the ...
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### Name of this formula or more explantation of the proof?

I have found this formula which is a combinatorial identity for counting binary words. I'd like more information on it, or the name of the proof. I am also not totally clear on the step between the ...
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### Probability of having n more 0's than 1's in a subsequence

We have a number K>2 and a sequence of m binary values $$b_1, ... b_m$$ Given a subsequence $$b_i, ... b_j, i>j$$ we define: W(i,j) is the number of 1's in the sequence L(i,j) is the number ...
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### largest number machine number that this comp has, numerical analysis, mantissa

I am having trouble understanding the basics on how to calculate the m, s and c of the formula. I have looked in my textbook but not much of an explanation, also on the IEEE websites but nothing much. ...
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### How to perform binary transformations?

One of the steps in Binary Index Tree algorithm is to find a node's parent which is done by un-setting the rightmost SET bit. For example: if a node has index 1010 than it's parent is 1000. To apply ...
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### Finding the maximum XOR metric

I'm trying to find a way to find n keys (x bits) where the XOR distance metric between them would be greatest. By XOR distance metric I just mean the value when two keys are XORed together. So for ...
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### Predict binary occupancy vector from history of vectors

I have a set of binary vectors where each vector represents one day of occupancy in a house and consists of 48 elements (each element for 30 minutes of the day). Each element can be 1 meaning that ...
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### Fixed decimal point numbers binary representation

I saw this formula that I cannot understand how it applies (the proof). Q: say we have a $N$ bit register (imagine a binary number with $N$ digits) for representing fixed decimal point numbers. In ...
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### System of equations with binary variables

Is there any way to simplify solving system of equations, assuming that all variables are binary? All equations, however, are seen as equations with real (or, to make things simple, integer) variables....
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### interpret reduced cost of all binary variables

I have prepared and run a Linear Programming model in SAS. I have some questions about the output that I canâ€™t find answers to, and am hoping that someone can help. My model contains the decision ...
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### 1s surpassing 0s in binary strings of odd length

Let $A(k)$ be the number of distinct binary strings of length $2k+1,$ for which the number of $1$s surpasses the number of $0$s for the first time at digit number $2k +1$, i.e., in the final digit in ...
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### Recurrence relation for the digits of the integer square root in binary

I was investigating a question on the Electrical Engineering Stack Exchange site, available here: http://electronics.stackexchange.com/questions/29311/calculating-the-square-root-of-8-bit-binary-...
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### Product of two binary numbers produce a string of 1

If $$x_i = 2^n + \sum_{j=0}^{n-1} x_j 2^j \;\; i \in {1,2},$$ Is there an easy way that maybe I'm not aware of to find the number (just the number) of solutions such that  x_1 x_2 = 1\ldots10\...
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### How generic is the “Unix file permission” algorithm?

In data analysis tasks, binary variables are usually encoded as $1$s and $0$s. In data sets with multiple binary variables, it is often necessary to create "interactions" of binary variables that can ...