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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2answers
20 views

Quaternary numeral system: fractions

I have a question related to the expression of a real number in base 4. Consider the table here: it is clear to me how all columns of the table are obtained except the fourth one: how do they get the ...
-4
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4answers
515 views

Why do they call it base 10?

Now, I know intuitively why it's called base 10: because there's 10 numbers. But see here's the thing, if we're working with numbers 0-9 (and of course we are), we use up our numerical artillery at ...
0
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1answer
25 views

How number system works in cases of hex, bin, dec and oct?

I have this question or a confusion from college time. When we convert a decimal digit to binary, we divide the decimal digit with the base of binary number system. Why there is no similar method ...
0
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1answer
15 views

How to calculate after decimal point of 99.21(Base 10) to (Base 8)?

As I know by 0.21 x8 and -4 for the answer to convert to base 8. However, I could not calculate and keep on expanding the value to millions.
1
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1answer
21 views

Expressing fractions in different bases. [closed]

In particular, a fraction that, in a certain base, will be recurring - such as $\frac12$ in base 3. (I used a base changing calculator to find it out) I have tried using repeated multiplation as ...
1
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2answers
142 views

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 ...
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2answers
34 views

Convert this into fractional number step by step?

3.41287548754875... Convert the above number to a rational number? I was reviewing some pre calculus on my own but couldn't figure this out.
0
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2answers
17 views

Alternative decimal number representation

In class we had an overview of different representations of numbers. Some examples were: decimal, roman numerals, binary, Redundant binary representation, church numerals... Then the teacher gave an ...
2
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2answers
39 views

Mayan Number System Explained.

I have recently been studying the Mayans and have encountered their number system. A dot represents 1 A line represents 5 A shell represents 0 The base of the number system is 20 During my ...
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2answers
387 views

Is PA the first axiomatization of arithmetic to be discovered? [closed]

Is Peano Arithmetic the first axiomatization of arithmetic to be discovered?
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1answer
63 views

How many ordered pairs (x, y) exist which satisfy the following equation? Both x and y are whole numbers. [closed]

$x \cdot\ y=2^2\cdot\ 3^4 \cdot\ 5^7 \cdot(x+y)$ I have tried rearranging the equation to different formats but not getting anywhere.
0
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2answers
37 views

Converting from decimal to any number base.

I know that this can a silly question. But I can not find the answer. When converting number bases (from decimal to any other number bases), we divide the decimal number by that base, and write down ...
2
votes
1answer
53 views

Can every real number be written as unique infinite decimals?

A slightly variation of this question: Can every real number be represented by a (possibly infinite) decimal? Here I restrict my discussion into infinite decimals (without ending with infinite zeros ...
2
votes
1answer
91 views

What's the real life purpose of Knuth arrows?

I recently read about Knuth's Arrows. Didn't even know those operations existed. My questions is: Do they have real-life applications? Most of the times a mathematical development follows a real-life ...
0
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1answer
15 views

converting fraction into binary by division

So i have a question regarding converting from farctions into binary decimals. if i have $\frac{3}{17},\frac{2}{9},\frac{1}{7}$ How can i convert those fraction into binary decimals using divison. ...
1
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1answer
38 views

What does leading $0s$ in a number in scientific notation mean?

Source: Computer Organization and Design: The Hardware/software Interface, David A. Patterson,John L. Hennessy It doesn't seem as the author is using leading $0$ like leading $1$ in a matrix. What ...
2
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1answer
39 views

Are there names for any of these four classes of numbers related to divisors and totatives?

Are there names for any of these four classes of numbers related to divisors and totatives? A [insert name here] of $n$ is a positive integer $\leq n$ that isn't a divisor of $n$ and that can be ...
1
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1answer
60 views

a*b = a/b = b/a (what's this symmetry called?)

I was playing around with numbers the other day, and I found an interesting symmetry, that I would like to know if it has any specific name assigned to it. Let's assume the notation n:a to refer to ...
0
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1answer
22 views

Delectable numbers in other bases

So there's a pretty useless number called the delectable number. A delectable number has nine digits, using the numbers 1-9 once in each digit. The first digit of a delectable number must be divisible ...
1
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2answers
108 views

How to prove that every power of 6 ends in 6?

Yesterday I had the traditional math matriculation exam, and in it there was a question "In what digit does the number $2016^{2016}$ end in?" After the test The Matriculation Examination Board ...
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2answers
32 views

Let $x \in \mathbb{R}$. Then $x^2 < x^3$ if and only if $x > 1$ [closed]

I am having a problem with proving this statement. Any help would be appreciated! Thank you
2
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0answers
112 views

Base ten representation proof

I want to prove that the pattern repeats but I can't figure out how.. Any help would be deeply appreciated!
0
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0answers
16 views

Given a base, a mantissa size and a range for the exponent, what's the largest number?

I was introduced to floating-point numbers week ago or so, and although I think I understood the basics, I'm still not sure how to apply them. A floating-point number is usually represented with the ...
6
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4answers
120 views

Could we “invent” a number $h$ such that $h = {{1}\over{0}}$, similarly to the way we “invented” $i=\sqrt{-1}$? [duplicate]

$\sqrt{-1}$ was completely undefined in the world before complex numbers. So we came up with $i$. $1\over0$ is completely undefined in today's world; is there a reason we haven't come up with a new ...
1
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1answer
42 views

Inequalities (Natural Numbers)

Suppose that $1 < x$ and $z < x^{z}$ is true where $x, z \in \mathbb{N}$. Prove that $z + 1 < x^{z+1}$. I have tried to use every inequality but have not been able to find the proof. This ...
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1answer
39 views

Defective coin weighing problem and ternary representation when number of coins is not a power of 3

We are given $N$ coins and a set of scales. We are told that there is a defective coin and we know whether it is lighter or heavier than the others. Our goal is to identify it in as few weighings as ...
3
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3answers
68 views

The last two digits of $13^{1010}$.

$13^{1010}$ $13^{\phi(100)} \equiv 1 \mod 100$ $13^{40} \equiv 1 \mod 100$ $(13^{40})^{25} \equiv 1^{25} \mod 100$ $13^{1000} \equiv 1 \mod 100$ $13^{1010} \equiv 13^{10} \mod 100$ That's all I ...
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0answers
16 views

rows of pascals triangle as powers of 11 in different numeral systems

It's not too difficult to see that (and understand why) in a base n system the ciphers of $(11_n)^k$ are equivalent to the k-th (0-indexed) row of pascals triangle until one of the numbers becomes ...
0
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1answer
34 views

What's the technical term for “place-value”?

When talking about positional notation, is there a technical term for "place-value" (as in, "the place-value of the 9 in 792 is 10), or is that it? Somehow, "place-value" sounds informal, but I don't ...
2
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1answer
44 views

Converting Integers from One Base to Another Digit by Digit

So I’ve done some hands-on work with converting integers from one base to another using the well-known method of division and taking the remainder. The most generic algorithm involves dividing the ...
0
votes
2answers
67 views

What is $346_7 + 165_7 $when expressed in base-$7$?

Hi I used a converter to do this question - and answered the second option. But still unsure, if I made it right.
1
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1answer
23 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 ...
0
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1answer
22 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
938 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) = ...
1
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1answer
28 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
87 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
63 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 ...
-2
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1answer
54 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
47 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
vote
1answer
47 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
votes
1answer
155 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
votes
0answers
104 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 ...
0
votes
2answers
40 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
42 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
101 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 ...
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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 ...
2
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0answers
32 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
18 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 ...
0
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3answers
54 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
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1answer
44 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 ...