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
15 views

Numbers that have constant digits value independent of base

I was wondering why for example $\dfrac{1111_b \cdot 111_b}{11_b \cdot 1_b} = 11211_b$. Is there a good explanation for this and is there a name for products like this which have constant digits value ...
1
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0answers
48 views

No square has a decimal expansion ending in 79

Show that no square number has a decimal ending in 79. More generally, find all possible two-digit endings for squares. Let any digit number ending at 79 be represented as $$a_nx^n+.....+7x+9$$ Plug ...
3
votes
1answer
47 views

Relationship between decimal length and Fibonacci number

There are 6 single digit Fibonacci numbers. For all other number of digits in the decimal system, there are either 4 or 5 Fibonacci numbers. For example, between 10000 and 99999 there are 5: 10946 ...
1
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2answers
77 views

Numbers divisible by $11$ [duplicate]

A number is divisible by $11$, when the difference between the sum of the digits in the odd positions counting from the left (the first, third, ....) and the sum of the remaining digits is either 0 or ...
0
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2answers
35 views

Convert the following between octal, decimal and hexadecimal

(a) Convert $61502$ from base $8$ to decimal. (b) Convert $EB7C5$ from base $16$ to octal. My answer: a) $6\times8^4+1\times8^3+5\times8^2+\times8^1+2\times8^0=25410$ b) not sure: converting $E=14$,...
1
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3answers
75 views

Converting from base $2$ to base 3

Transform the binary expansion $y = 0.110110110\ldots$ into a ternary expansion. We are given that $y = 0.110110110\ldots_2$ and thus $1000_2y = 110_2+y \implies y = \frac{6}{7}$. Then we see that $\...
2
votes
1answer
16 views

Decimal representations of the reals both 1-1 and order-preserving?

The conventional representation of the non-negative reals as infinite decimals is 1-1 for numbers which are not multiples of $10^{-n}$ for some $n$, and 2-1 for numbers which are (for example, $0.2999....
5
votes
4answers
859 views

Roman Numbers - Conversion to decimal number

I have read that if a smaller number is to the left of a larger number means that the smaller number has to be subtracted from the larger number. Ok I can understand quickly for below Roman Numbers : ...
14
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5answers
2k views

How can I tell if a number in base 5 is divisible by 3?

I know of the sum of digits divisible by 3 method, but it seems to not be working for base 5. How can I check if number in base 5 is divisible by 3 without ...
3
votes
6answers
147 views

Find the rightmost digit of: $1^n+2^n+3^n+4^n+5^n+6^n+7^n+8^n+9^n$

Find the rightmost digit of: $1^n+2^n+3^n+4^n+5^n+6^n+7^n+8^n+9^n(n$ arbitrary positive integer) First of all I checked a few cases for small $n$'s and in all cases the rightmost digit was $5$, so ...
0
votes
2answers
37 views

Is it an overflow or not?

The addition of 4 bit, 2's complement binary numbers 1101 and 0100 is $$\begin{array} \\\hphantom{+}1101\\ + 0100\\ \hline \\ 1 \ 0001 \end{array}$$ there occurs a carry out above, but this will ...
1
vote
0answers
31 views

Convert floating point number to short int [closed]

This is the transfer function of a FIR filter $$H(z) = -0.125 + 0.25z - 0.125z^2$$ How to convert the coefficients to short int? Is it correct if I just multiply ...
1
vote
2answers
32 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 ...
0
votes
4answers
556 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 9....
0
votes
1answer
27 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
votes
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
vote
1answer
25 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
146 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 ...
0
votes
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
votes
2answers
21 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
votes
2answers
44 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 ...
4
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2answers
390 views

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

Is Peano Arithmetic the first axiomatization of arithmetic to be discovered?
-3
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1answer
67 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
votes
2answers
49 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
57 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
100 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
votes
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
vote
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
votes
1answer
41 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
votes
1answer
27 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
vote
2answers
126 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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votes
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
votes
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
votes
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
votes
4answers
121 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
vote
1answer
45 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 ...
0
votes
1answer
41 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
votes
3answers
74 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 ...
0
votes
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
votes
1answer
38 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
votes
1answer
50 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
vote
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
votes
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
votes
3answers
947 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) = a^4+4a^3+6a^2+...
1
vote
1answer
33 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
91 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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votes
1answer
65 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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votes
1answer
60 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 ...