# Tagged Questions

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

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### Binary representation with more coefficients

Given a positive integer $n$, how many ways are there to write it as $a_0+2a_1+4a_2+\dots+2^na_n$ such that $a_i\in\{0,1,2,3\}$ for all $i$? If the coefficients were allowed to be in just $\{0,1\}$, ...
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### Algorithm to convert binary fraction to decimal fraction

There's an algorithm to convert binary integer into decimal integer that is based on the expanded form of a number: $$12 = 2\cdot(2\cdot(2\cdot(2\cdot 0 + 1)+1)+0)+0$$ \begin{aligned} & 2\cdot0+...
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### The use of binary numeral system for theoretical results

I wonder how mathematics would be changed if we were been using binary system in calculations instead of decimal .. Could theory of mathematics would change a little ? Are there known ...
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### Rounding - should I compare truncated sum with the number added to make least bigger number

Suppose I have a number in binary: $$0.11111 = 0 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32}$$ I want to round it to 3 significant digits after the radix point. So, I ...
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### How to find the least bigger number than the given one

I have the following number in binary: $$0.111_2 = 0 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}$$ I need to find the number such that it's bigger than the current and there is no number in between ...
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### How do I know that the number is halfway in between

I was shown the following: $$0.110 < 0.1101 < 0.111$$ and told that the middle number is halfway in between those two numbers. Is this correct? How can I see that? Update: If I add a zero ...
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### Why $82000$? Numbers that can be written from base $2$ to base $5$ using only the digits $0$ and $1$

This is really very curious. Many links on http://oeis.org/A146025 about this but -- why? I mean, this is not some abstract mathematical notation but rather something inherent in, I dunno, the ...
I have this number: $$0.2 = 1.1001100110011001100110011001100110011001100110011010 \times 2^{-3}$$ I want to have the exponent to equal -4. Should I just move ...