# Questions tagged [binary]

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

1,170 questions
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### Can we write $2^\alpha$ as sum of smaller 2-powers when $\alpha\geqslant 5$ is a positive integer?

Let $\alpha$ be a positive integer $\geqslant 5$. Let us consider \begin{align*} &B_1\subseteq \{0,1,2,3,4\}\\ &B_2\subseteq \mathbb{N}-\{0,1,2,3,4\} \end{align*} where $B_2$ can be finite or ...
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### I need to solve one equation, but I dont know how to solve equation with floor functions

Im a student with not such a knowledge to solve equations with floor functions. I want to ask, if it is even possible and if it so, how is possible to prove this equation to be true. ...
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### 24-bit Binary to single precision floating point number

I have the 24-bit binary: 0101 0011 1111 1101 0111 1101 And I need to figure out: What pair of single precision floating point (real) numbers could be represented by these 24-bits? I'm fairly ...
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### Proof of the duality principle in Boolean Algebra

I have looked at some proofs of the duality principle online, and those use a lot of algebra which I do not understand. Is there a simple proof of the duality principle? I know the basic laws, ...
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### Generating function for special string 11100

Let $S$ be the set of $\{0,1\}$-strings that do not contain $11100$ as a string. Find the generating function of S where the weight of a string is its length. I tried this way : Consider all blocks ...
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### Are there any non-trivial examples of this decimal-binary property

My birthday is 10th of October or 1010 in MMDD format. I just realized that 1010 contains two copies of the number 10 and if spelled out in binary, $1010_2=10$ I was wondering how many other ...
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### Is the dimension of a binary linear code the number of codewords it contains? [closed]

For example, would the dimension of the binary linear code $\{0000,1111\}$ be $2$?
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### Finding similarities between binary strings

I have been tasked with this puzzle for my programming class, it's purely a puzzle and doesn't count towards any grades, but not being able to solve it is really bugging me! We have been given two ...
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### Prove that the mapping of a number to its XOR with some constant c is bijective

Prove that $x \mapsto x \oplus c$ is a bijection over the range $[0, b]$, regardless of the value of constant $c$, where $b = 2^{k} - 1, k \in I^{+}$.
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