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 ...

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1answer
20 views

Convert base y to base 10

I have a problem to find base y. The equation given is ($1111011$)gray + ($123$)y + ($211.1$)3 + ($34.4$)$6$ = (CD)$16$ + ($40$)y - ($10010$)BCD. I am able to simplify by converting everything ...
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1answer
20 views

Vocabulary: numeral system where “||” represents “2”

A useful system in some contexts where are you counting things is writing 1 as | 2 as || 3 as ||| . . . 11 as |||| |||| | Example of usefulness is keeping track of ...
18
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3answers
900 views

Prove that the number 14641 is the fourth power of an integer in any base greater than 6?

Prove that the number $14641$ is the fourth power of an integer in any base greater than $6$? I understand how to work it out, because I think you do $$14641\ (\text{base }a > 6) = ...
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1answer
22 views

Hexadecimal arithmetic on calculator (casio etc.)

When I do hexadecimal subtraction say, 2A-324 on a casio calculator or any calculator in general, i get the result as FFFFFD06 Why do i get so many F's ?? dosnt F stand for 15 in hex. In any general ...
0
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1answer
63 views

What does “within the same order of magnitude” convey?

This question originates from a quandary about the meaning of the statement that two values are within the same order of magnitude. I wonder whether there is an established usage, of (rather more ...
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1answer
51 views

why is F+9 = 18 ? although F is equal 15? [closed]

this is still in number systems but in adding hexa decimal why is F+9 = 18 ? isn't F = 15 (A=10,B=11,C=12,D=13,E=14,F=15)? and 9 is just 9 ? here is the sample question add 1 C 9 with B 2 F and the ...
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1answer
43 views

why octal number system jumping from 7 to 10 instead 8?

I know the question is really confusing but I have a questin about Octal number system. I am reading a book and on the counting in octal as shown 0,1,2,3,4,5,6,7,10,11,....,16,17,20 ? why does the ...
1
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1answer
33 views

What is the standard : long or short scales

I know about long and short scales of numbering systems, but I want to know, what is the standard naming of large numbers?!! is that back on the long scale or the short scale?!! so if someone in the ...
1
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1answer
44 views

Hexadecimal numbers that does not look like decimal

Given a range of hexadecimal numbers, how do I determine the total number of them that do not look like decimal numbers? Background: I'm designing a system that auto-generates IDs that consist of ...
3
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1answer
137 views

Uniquely identify any finite subset of an infinite set

Let $U$ be an unbounded subset of $\mathbb{N}$. Let $D = \mathcal{P}_{<\omega}(U)$ (the set of all finite subsets of $U$). Let $f$ be an injection such that: $f: D \rightarrow \mathbb{N} $ ...
3
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0answers
103 views

Having $\pi$ fingers and count [closed]

The number $\pi$ has infinite decimals whom appear to be randomly distributed. If we had $\pi$ fingers, and would therefore use $\pi$ as base instead of ten, could I then count integers on my ...
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2answers
38 views

Finding some rational numbers

Let $p$ be a prime number and let $x$ be a rational number such that $x>1$. Prove that if $x^2<p$, then there exists a rational number $z$ such that $x<z$ and $z^2<p$. (Please, don't say ...
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4answers
37 views

Finding Rational numbers

Let $w$ be a positive rational number and $w^2>2$. Prove that there exists a positive rational number $x$ such that $x^2>2$ and $x<w$. A condition is you can not use the property of real ...
0
votes
3answers
91 views

What makes it clear that 1 precedes 2?

In the construction of natural number system, I'm not sure how the ordering of elements of N is defined. It seems that almost every approach to that is quite abstract without mentioning an actual ...
1
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0answers
37 views

Numbers $n$ whose prime factors are $2$ and $5$ if and only if $\sum_{k=1}^{rad(n)}\mu(k)k=0$?

In the literature if defined the arithmetical function $rad(n)$ as $1$ if $n=1$ and for $n>1$ by $rad(n)=\prod_{p|n}p$. It is obviously a multiplicative function. Too we know the Mobius function ...
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0answers
26 views

Are there any numeral systems that start with 1x prefix?

I know that it is customary to prefix hexadecimal numbers with 0x. I came across this number 1X000008 and was wondering if it is ...
1
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0answers
15 views

binary divison with remainder

I wanted to calculate this (binary): 10101.101/1.1. the result is: 1110.01101010101010101010101010... I succeed in calculating the integer part, but I didn't understand how I find the numbers that ...
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3answers
43 views

Why are every number (integer) exactly divisible by 5 in decimal number system but not in binary number system?

I have wondered during the number system classes in computer science that if 1/5 in decimal number system results in 0.2 why ...
0
votes
1answer
40 views

At what base is square root of 120 natural number

I got this problem i need to solve: At what base b, where b>2 , (120)b equals x2, where x is in decimal number system? I need to find all bases b, and i need to see the process of finding answer, so ...
8
votes
2answers
924 views

Is there any basis transformation under which all irrational numbers are rationals and vice-versa?

For example, if you change the length of your "unit scale" or basis for numbers to $\sqrt{2}$, then you may represent all fractional multiples of $\sqrt{2}$ as "rational numbers" in the new basis ...
0
votes
1answer
23 views

permutations of binary sequences

What is the proof that there are $2^n$ distinct binary codes of length n I know this progression also applies to the decimal ($10^n$) and hex ($16^n$) systems but how can this be shown?
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1answer
51 views

Does the Look and Say sequence have terms with odd number of digits? (also for other bases)

I had just put up a question on Puzzling SE about the Look and Say sequence. I was just curious. In the base-2 sequence, some terms had an odd number of digits. Does the normal base-10 sequence have ...
1
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1answer
64 views

Does $625!$ have $156$ zeros at the end?

Someone wrote that $625!$'s last $156$ digits are zeros because $125+25+5+1=156$. If it's true that $625!$ has $156$ zeros at the end, how does "$125+25+5+1=156$" prove it?
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3answers
99 views

Addresses in decimal,binary,octal and hexadecimal

One of the first minicomputers, the PDP-8 had a word size of 12 bits. (Recall the word size of a computer refers to the number of bits used to encode addresses.) what was the last address in this ...
2
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1answer
39 views

Find max(x) in ${ 2 }^{ n }={ \left( \underset { x }{ …\underbrace { aaa..aa } } \right) }_{ 10 }$

I've already spent 2 hrs on this question but can't find,but I'm pretty sure there is a mistake in this question,or is this possible? $$ n \in \mathbb{Z} $$$$ { 2 }^{ n }={ \left( \underset { ...
0
votes
1answer
35 views

Question on Converting between Base Number Systems

Question on Converting Between Base Numbers The people of Jupiter use Base 13. Therefore, their numerals are 0,1,2,3,4,5,6,7,8,9,A,B,C. The people on Saturn use Base 7. Therefore, their numerals are ...
2
votes
1answer
96 views

Can $\pi$ be rational in some base radix

I am from a physics background and my mathematics is not very good, so pardon my insolence with the question. Editing based on the comments : We know that $\pi$ in decimal (i.e. base 10) is ...
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2answers
61 views

Calculating last digit of a number using binomial theorem

How to calculate the last digit of a number say like $$\large 3^{4^{5}}$$ using binomial theorem? P.S:I know how to solve it using modular arithmetic. I saw this one but its not of much use in ...
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votes
1answer
35 views

Base Number Arithmetic [closed]

I got no idea how to solve that problem. What I have done so far is I have randomly guessed numbers. I wanted to know a faster way to solve it in the future, just in case of some even more complex ...
0
votes
1answer
28 views

How to apply digit sum checks with modulo?

How can you use a "digit sum check" modulo $\beta - 1$ or $\beta + 1$ to prove that an operation is faulty or incorrect? For example, given the expression below where base $\beta$ is 5: $142\bar3_5 + ...
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2answers
63 views

Converting a number from one base to another without going through base 10.

I have a problem. I am very good at converting numbers from base to base after going through base 10. The question is, how can I do the conversions without going through base 10? Thanks
0
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1answer
44 views

Is this sum of Binary Numbers an Overflow?

I have a question of the likes of 21 + 11 I converted each number to binary getting: 010101 + 001011 I got a result of : $100000$ which is $32$ in decimal Thus it is correct that $21+11 = 32$. ...
0
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2answers
22 views

How many binary numbers can be represented with X number of number places?

How do we find out that in the binary number system, how many different numbers can be represented with a certain number of number-places? For example, suppose we have 8 number places, i.e. a 1's ...
14
votes
1answer
133 views

Multiplication of doubly-infinite decimal numbers

Summary of the question: Doubly-infinite decimal numbers are "numbers" whose decimal expansions are allowed to extend infinitely both to the left and right of the decimal point, for example ...
1
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3answers
57 views

Show that $n-m$ is a multiple of 9 when $n$ and $m$ have same digits

I have just proved the divisibility rule for 3 and 9. Let $n\in\mathbb{N}$. Let $m$ be a number that appears when you shuffle the digits in $n$. Show that $n-m$ is a multiple of 9. Can anyone offer ...
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0answers
34 views

Solving the heat equation with enthalpy method

I have a problem that I truly hope won't be much of a burden to you. It may be straightforward for some of you, but it's not for me. It's been troubling me for days. I have an ice cube of lenght L, ...
0
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1answer
30 views

Equations with different numerical systems

Before all, good morning; I have just seen an exercise of number systems and equations... I hope you could help me with this: An equation is given: $$6x^2+60x+150=0.$$ The exercise says that this ...
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1answer
95 views

Uniqueness of binary representation

how to prove that binary number is always represent unique decimal number? (uniqueness of binary system) i.e every binary number determines unique decimal number i.e there is one-to-one relationship ...
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1answer
58 views

In what base would $\pi$ have the fewest decimals? [closed]

What is the numeral system in which $\pi$ would have the lowest number of decimals possible?
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2answers
51 views

which is the more accurate way of representing numbers?

When we consider calculations at tiniest of scales which number system would be more accurate, when we consider the binary number system( base 2) or the number system we generally use (base 10). The ...
1
vote
1answer
46 views

Convert from base 10 to base 5

I understand the integer part, keep dividing by 5 and I get 112, but for the fraction part I need a help. The number is: $$ (32.\bar 5)_{10} = (112, ??)_{5} $$ $$ 0,5 * 5 = 2,5\\ 0,5 * 5 = 2,5\\ ...
0
votes
0answers
33 views

Is there a name for complex numbers over affinely extended reals?

Is there a name for the set of complex numbers over affinely extended real line, that is $\mathbb{C}\cup \{-\infty\}\cup\{+\infty\}$? I think this set is the most commonly used in analysis ...
3
votes
2answers
113 views

Is a decimal number system the best to grasp mathematics?

I am often amazed by how accurate a decimal numeral system is to describe the mathematics world. A lot of things feel very logical like the ...
0
votes
1answer
72 views

What is the significance to our number and degrees systems? [duplicate]

I saw this video recently and it suggests that there is some "magical" reason that there are 360 degrees in a circle and that it is also connected with our number system. My question is: How did we ...
1
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1answer
37 views

Representing numbers by quasilexicographic ordered strings, formula for size of conversion between different alphabets

Let $X_r = \{ 0, 1, \ldots, r-1 \}$ and $X_b = \{ 0, 1, \ldots, b-1 \}$ be two finite alphabets with order's given by their numerical value. Consider the quasilexicographic (or shortlex) order on ...
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4answers
138 views

How many $0$s does the number $30!$ have? [duplicate]

I want to find out the number of $0$s in the number $30!$, what should I do? Is there any trick that would work for a general question of this type, like number of $0$s in $50!$ ?
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2answers
149 views

Why does our number system have only 10 different symbols? [duplicate]

To be specific, I am just curious as to why does our number system have 10 different digits?Just for an example, why did it not end at 7? (it is the greatest prime number before 10, there are 7 days ...
0
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1answer
18 views

How to remove $1$ at position $x$ ( in base $B$) from a number represented in Base $10$

I was going through a solution on code chef in which we needed to remove a $1$ from a position say $x$ (in Base $B$) from a number in Base $10$ if the representation of that number in base $B$ had a ...
1
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1answer
53 views

Is the cubic formula numerically unstable?

Are there numerical rounding issues in using the cubic formula to find roots of cubic equations? Similarly with the quartic formula? I do know for the quadratic formula to solve $ax^2+bx+c = 0$ that ...
1
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0answers
56 views

Is our Arabic number system based on a geometric design counting corners? [duplicate]

The following writer asserts that our system of Arabic numerals is a geometric design where the number of corners corresponds to the number represented: My question is: Is our Arabic number system ...