# 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 'unique' one bit binary functions with N-bit inputs

Consider the set of binary functions that takes an N-bit input -> 1 bit output. There are 2^(2^N) elements in this set. Now potentially reduce this set by restricting to only considering functions ...
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### truncation in two's complment

My textbook gives an example of truncating a signed number in two's complement from 4 bits to 3 bits. It truncates -4 to 4. I am little confused by this, because the binary representation of -4 is ...
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### Inverse of binary matrix

I have tried creating an inverse of a binary matrix using the identity matrix method. Have an identity matrix alongside the square matrix and perform all the operations to convert the square matrix to ...
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### Converting from base $x$ to base $y$

I'm trying to convert from base $x$ to base $y$, but am having trouble understanding why the following method only works when converting to base $10$. Take for instance the number $2132$ (base $4$). ...
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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 ...
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### How to convert numbers with related bases quickly?

Let: $a = (1011011)_2 = (1123)_4$ There two ways to solve it: Convert the number in base 2 to base 10 then to base $4$. Consider $4 = 2^2$ and group each of two numbers in base $2$ to one in base ...
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### mutual information and combinatorics

\begin{align} &\mathrm{H}\left(\frac{1}{2^{k}}\right) \\[3mm]&\ \!\!\!\!\!\!\!\!\!\! - {1 \over 2^{k}}\left\{% {k \choose 0}\mathrm{H}\left(\left[1 - \epsilon\right]^{\,k}\right) + {k \choose ...
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### Data Representation Question

A computer stores a number of $16$ bits word using floating-point arrangement. Given that the first bit is reserved for the sign and followed by $6$ bits for the exponent using biased form. The ...
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### Is there any kind of known pattern to $\sqrt 2$ in base 2?

Is there any kind of known pattern to $\sqrt 2$ in base 2? Is there any classification categories for decimal digits of numbers that for example would put $\sqrt 2, \sqrt 3 \cdots \sqrt n$ into ...
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### Partitioning binary strings by total parity

If I have a binary string $\underline{a} = (a_1 \, a_2 \,\ldots\, a_N)$ where $a_i \in 0,1$ and I partition the set of all such strings $A$ by the total parity of the string, $A = \Pi_0 + \Pi_1$ where ...
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### What is the purpose of Excess-K representation?

What is the purpose of excess-k when representing binary floating point binary numbers. I came across this in my computer systems course and I can't figure out the advantage of offsetting the numbers ...
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### Proving that $A+B - (A \cap B) = A \cup B$ for binary integers

I hope computing questions are fine here. I'm trying to show that for all binary numbers $A$ and $B$, $A+B - (A \cap B) = A \cup B$. It's confusing me firstly because I'm not sure what the "set ...
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### Combined probability of hit in look up tables with some common index bits

Consider two tables A and B consisting of $l_a$ and $l_b$ counters respectively - $l_a$ and $l_b$ are powers of two and the counters are initialized to zero. Each table has its own index ...
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### XOR equation with multiplication arrangment

How can I move all the X to one side so the equation will become x=y XOR <somthing>... \begin{align} &2x \oplus y = x \end{align} ...
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### Negative representation of a binary number

I saw online that if you want to convert a binary number to a negative binary number, you add 1.However, I don't understand why you do that.In a forum I saw someone explaining the following: ...