# Questions tagged [binary]

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

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### how to convert decimal 49.25 to hexadecimal?

please explain step by step procedure on how to convert 49.25 to hexadecimal. I don't understand how to convert the decimal part.
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### Minimum number of nodes perfect binary tree

definition of perfect binary is "which all internal nodes have two children and all leaves are at same level" perfect binary tree i know max. node number: 2^h - 1 (h>=1) but i cant figure out, ...
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### About binary subtraction: how does this work?

So there's a course I'm watching online and it operates binary subtraction this way: asking y-x, where: y=0111 (or decimal 7) x=0010 (or decimal 2) And instead of using a 2's complement to change ...
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### Binary multiplication 1111 x 1111?

I am confuse that how carry works while multiplying two binary numbers 1111 x 1111 = 011100001 but how to handle carries in calculation? Can anyone please explain? I know how to handle partial ...
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### 3.1 x 10^-9 in 4-bit sign-magnititude representation problem possible?

I'm puzzled with this math question below and would like the help of others, the only answer I can imagine to this question is that the above number will need more than 4 bits to be expressed in ...
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### Highest power of 2 factor of $N!$ is equal to $2 ^{N - {\rm sum\ of\ bits}}$?

I am reading on this page a formula stating that the largest power of 2 contained (as a factor) in $n!$ has the following exponent: $n -$ number of bits that are equal to $1$, in the binary ...
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### Rational numbers with repeating decimals in binary

Is it possible to prove that there exists a rational number with repeating decimal digits in base-10 representation that isn't repeating in binary? For example, $0.\overline{0011}_2$ is a binary ...
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### Elegant way to obtain the smallest subset of binary matrix rows where each column sums to at least 1

Context: I have $m$ groups of a random number of $n$ types. Each type can occur only once for each group. I hope to reduce the groups to the smallest set such that each type occurs at least once. ...
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### Help on computing some property value of a binary tree.

I am trying to compute some properties of a binary tree, but I cant find its formula. What I did to get the initial value is, I draw the binary tree on paper and manually count the nodes, pairs, etc. ...
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### Probability of binary string prefix divisibility by 3

What is the probability of an evenly distributed binary string of length $n$ to have a prefix that is divisible by $3$? I know that divisibility by $3$ of a binary string is equivalent to the ...
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### Algorithm and Generating expressions that satisfy a condition

def dec_to_bin(n): s = '' x = n while x > 0: d = x % 2 x = x // 2 s = str(r) + s return s What does expressions $A$ and ...
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### Transforming a combinatorics question to a binary system question.

Preface This is a quite interesting question that I have come across some earlier years in my Olympiad training. Due to my bad memories and notebook record, I failed to trace back where I found this ...
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### What is the notation of a set of $n$ binary numbers where all of them are 0 except for one?

From this post I found out we can define a set of $n$ binary numbers mathematically like: $\mathbb Z_2^n$. But what if I want to further restrict this set such that all the bits must be zero except ...
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### how to generate variates from a particular categorical binary data?

So im working with more than 100 thousand samples dota2 dataset which consist of the winner and the "hero" composition from each match. I was trying to build winner of the match prediction model ...
### Prove $\big\lfloor{\frac{n}{2}}\big\rfloor+\Big\lfloor\frac{\lceil\frac{n}{2}\rceil}{2}\Big\rfloor+\cdots = n - 1$.
I suspect for $n\in \Bbb{Z}^+$, and $\lceil{log_2n}\rceil$ addends, \$\big\lfloor{\frac{n}{2}}\big\rfloor+\Big\lfloor\frac{\lceil\frac{n}{2}\rceil}{2}\Big\rfloor+\Bigg\lfloor\frac{\Big\lceil\frac{\big\...