Questions tagged [number-systems]
Representations of numeric values in decimal, binary, octal, hexadecimal, and other bases; one's-complement and two's-complement signed numbers; scientific notation; floating-point numbers in digital computers; history of number systems; nonstandard number systems; algorithms for arithmetic within specific number systems or for conversions between number systems.
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Finding rational numbers between a pair [closed]
I was trying to find out rational numbers between a pair of p/q number.
On youtube a tutor told to "add 1 to the number of rational number we want to find out" say we want 5 so 5+1=6. so now ...
- 19
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2
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Is there a term for a number system where the digits can have any value you want? [closed]
Before, I had the idea of a number system where the digits can have any value you want, for example:
$$11 \langle10^{24}\rangle = 1\cdot100 + 1\cdot10 + 10^{24} = 1,000,000,000,000,000,000,000,110 $$
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- 239
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Gray code permutation notation
I 'm trying to understand the notation of the Gray code permutation but since I only know 2-row matrix notation for permutations, I would like an explanation for the notations below . I understand the ...
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Looking for references for easy facts about Zeckendorf and dual Zeckendorf representations
I'm looking to find references to cite for some easy facts about Zeckendorf representations and dual Zeckendorf (aka lazy Fibonacci) representations. Most of these are definitely known because e.g. I'...
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(Basis Representation) How to Prove $b_k(n)\leq b_k(n-1)$?
NOTE: THIS QUESTION IS NOT A DUPLICATE! THE ANSWER IS NOT IN THE RECOMMENDED QUESTION LINKED TO THIS POST
Reason: While the recommended question does mention $b_k(n)$, it never addressee why $b_k(n)\...
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1
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Number in Base b as Dot Product
Question out of curiosity:
Any $k$ digit number $a_1 a_2 a_3 ... a_k$ written in base $b$ can be thought of as the dot product of a digits vector $a = \langle a_1, a_2, a_3, ..., a_k\rangle$ and a ...
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How to determine (possibly mixed radix) bases for which a number's representation is "digit-wise maximal"?
For some $n \in \mathbb{N}$ and (possibly mixed radix) basis $B$, let $\mathrm{repr}_B(n) = d_1d_2d_3\ldots d_m$ be the representation of $n$ in basis $B$. Call such a representation digit-wise ...
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Looking to improve an algorithm for decomposing an integer
I'm interested with primorial number system. In this playful setting, out of curiosity and for relaxation, as an amateur, not knowing the current algorithms for decomposing a $2$-almost prime number $...
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1
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How do you multiply in Primorial number system?
Primorial number system is a number sytem that uses primorials which are defined as follows :
Let $p_1=2, p_2=3,p_3=5,p_4=7,p_5=11,...$ the primes. The sequence of primorials, noted $p_n\#$ is $$(p_n\#...
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Help to mathematically theorize the eventual value of Primorial number system
The primorial numeral system is a numeral system whose interest I am trying to establish mathematically.
Unfortunately, my mathematical knowledge is limited, so I would like to briefly present some ...
- 3,286
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1
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Using Fake Numerals to Make Real Decimal Numbers [closed]
The setup to this question is very simple: Take the numbers $\frac{1}{1}, \frac{21}{12}, \frac{321}{123},...,\frac{987654321}{123456789}$ and plot them versus the natural numbers, as seen here: https:/...
12
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4
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Can a decimal that is infinitely repeating in one base be nonrepeating in another?
For instance, can a number like $0.1111111\cdots$ in base $3$ be represented as $0.23515613\cdots$ (non-repeating) in base $8$? I imagine the answer would be a resounding NO but it would be ...
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What is this field in $\mathbb{R}^4$ that contains both the real and complex numbers called?
Note: this question is wrong – this is not a field, though it is not obvious why it wouldn't be.
So, I (first year undergraduate mathematics student) was looking around the internet and found an ...
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On average, how many more digits do octal numbers have than decimal numbers? [duplicate]
My question is, how could I calculate the expected value of the number of digits of an octal representation of an $n$-digit decimal number?
How can this question be answered in general for two ...
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Reduce the base $11$ fraction $\dfrac{587}{749}$ to its lowest terms.
Reduce the base $11$ fraction $\dfrac{587}{749}$ to its lowest terms.
$(\dfrac{587}{749})_{11}=\dfrac{5\times 11^2 + 8\times 11 + 7}{7\times 11^2 + 4\times 11 + 9}$
But $\dfrac{...+7}{...+9}$ can't ...
