Questions on the different ways to represent a number, how to convert between those different ways, and other such questions. The usual system employed by humans is the decimal (base-10) system, but other systems like binary and hexadecimal are also in frequent use.

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2answers
63 views

What would be the problem in mathematics if there are no negative numbers in number line? [on hold]

We all know that $-\times-=+$, $+\times+=+$ and $+\times-=-$. $-\times-$ will mean add a negative number, say, $-a$, $-a$ times, which is going out of sense. Other two are easy to understand, add ...
3
votes
3answers
50 views

Is $(-1)^{1/8} + (-1)^{7/8}$ ever a value whose real component is $0$?

Is $$(-1)^{1/8} + (-1)^{7/8}$$ ever a value whose real component is $0$? Is this ever true in modular arithmetic, hypercomplexes, and/or both?
2
votes
1answer
44 views

How to convert base 7 to base 19 directly

Is it possible to convert base 7 to base 19 directly without first converting to base 10 ? If so, what is the algorithm ?
0
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0answers
34 views

Is this quantity always $1$ (in higher-dimensional algebras)?

If we are working with a Cayley–Dickson construction, with a dimension 16 or greater, is the following quantity always 1: $$e_x * e_y * (-e_y) * (-e_x)$$ In other words, if we multiply a number in ...
0
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1answer
23 views

Can we have an associative form of “octonions” and hypercomplexes, if we eliminate division?

I'm interested in hypercomplexes, or number systems with many square roots of $-1$. Now, I know that quaternions are non-commutative, but associative. I'm wondering if it's possible to have a number ...
1
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4answers
221 views

What is the definition of a positive integer?

I am reading the book "The Number-System of Algebra (2nd edition)". At the starting of page-4 the author writes: A positive integer is a symbol for the number of things in a group of distinct ...
0
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0answers
22 views

Roman to Decimal Number conversion

I am trying to convert CIIXMXCVCII to decimal number. However, I am not getting it completely if it's a valid roman number representation or not. I tried this online tool: ...
0
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0answers
19 views

A property/result which does seem to be dependent on number system but is independent.

Would you tell a property/result which does seem to be dependent on the number system(base) but is independent of the number base?
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6answers
374 views

What do we mean by the term “Number of things”?

I am reading the book "The Number-System of Algebra (2nd edition)." I have some problems with the the first article: "Number". The author has confined the concept of number of things to the groups ...
2
votes
2answers
24 views

Numerical System

This was my interview question in the question paper. please help me in finding the answer . " in a class of 100 students 24 of them are girls and 32 are not. Which numerical system base are we using ...
0
votes
0answers
30 views

Other Strange 'Magical' Numbers in Base 'x'

The number 9 has quite a few interesting patterns involving multiples. The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. The list of oddities ...
1
vote
3answers
169 views

Is $\epsilon^2/\epsilon^2=1$ or $0/0$?

Is it possible in the system of dual numbers ($a+\epsilon b$; $\epsilon^2=0$) to calculate $\epsilon/\epsilon =1$? How then does one deal with $\epsilon^2/\epsilon^2=1$ versus ...
5
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0answers
129 views

How find this $aA_{m+1}=\overline{\sigma_{0}\sigma_{1}\sigma_{2}\cdots\sigma_{m}}$

Question let $m$ is positive numbers,and such $m\ge 5$,and $$A_{m+1}=\overline{1234\cdots m}=1\times (m+1)^{m-1}+2\times (m+1)^{m-2}+\cdots+(m-1)\times (m+1)+m$$(or see ...
1
vote
3answers
81 views

Finding set of non recurring non terminating decimals

I need to find a set of two Integers P and Q such that ...
0
votes
2answers
57 views

Systems the Peano axioms can be derived in

I know that the Peano axioms can be got from ZF set theory, and lambda calculus. What other systems can they be derived (I'm not sure if that is quite the right word here) in, and which the simplest ...
0
votes
1answer
25 views

Range of number systems [closed]

I don't understand how to get the fraction part. This is what I came up with for the integer part. A) For 12 bit unsigned = 0 to 4095 B) For 12 bit signed = -2048 to 2047 C) For 12 bit in 2's ...
0
votes
0answers
28 views

Biased form with hidden bit

A computer stores a number of 16 bits word using floating-point arrangement. Given that the first bit is reserved for the sign and followed by 6 bits for the exponent using biased form. The remaining ...
0
votes
1answer
35 views

Data Representation Question

A computer stores a number of $16$ bits word using floating-point arrangement. Given that the first bit is reserved for the sign and followed by $6$ bits for the exponent using biased form. The ...
0
votes
2answers
76 views

Binary Code Decimal (BCD)

I need help with the following question, my try is at the bottom: Question : Using Binary Code Decimal 8-4-2-1 representation, calculate 6789 + 7156 - 365 My Answer : 1101010000101 + 1101111110100 = ...
1
vote
1answer
49 views

Base change system

the people in aldeeran planet use a base six system. a]show how the aldeeran people represent each of the following: i) 291.5 (base 10) ii) 1010111 (base 2) iii) 71.6 (base 8) iv) 10A.4 (base 16) ...
1
vote
2answers
45 views

Calculate mode of 2 numbers with the same base !!!!

I have 2 numbers with same base(not necessary 10). I want to calculate the mode(Remainder of the division) of this 2 numbers without changing the base of them.The base of this 2 number can be ...
2
votes
1answer
32 views

Proving Arithmetic

In mathematics if one is to prove a property of arithmetic, such as the associativity of addition, without going into greater detail about the numbers themselves, I feel like I'm missing something ...
0
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2answers
45 views

Are the extra digits for Base 32 and Base 64 standardized?

Hexadecimal is widely recognized with A - F as the digits beyond nine. However, what about bases with even more digits, such as Base 32 and Base 64? For Base 32, you could simply continue the ...
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2answers
46 views

A question about indeterminate forms

Are there any set of numbers into which any of the indeterminate forms we see in a calculus course, like 00, n/0, 1infinity, etc has an answer? I'm asking that because, thanks to the Net, I took ...
7
votes
1answer
72 views

Is it possible to have numbers that are to Hyperreal numbers what Hyperreals are to Reals numbers?

There are Hyperreal numbers that are smaller than any real number , also those that are larger than any real, they have properties analogous to those of Real numbers thanks to the Transfer principle ...
1
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1answer
50 views

IEEE-754 64-bit representation of any number between -1 and +1 [closed]

In 64-bit IEEE 754 format, a 64-bit number is represented using 1 bit for the sign bit, 11 bits for the exponent width, and 52 bits for the fraction precision. How many bits is used to represent ...
2
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3answers
200 views

If $5 \times 12 = 104$, how much is $10 \times 11$?

Question is in the title, this is for my analysis course. I don't know where to begin.
4
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1answer
75 views

A new type of numbers?

Humans started to think about solution to the equation x+2=0, they invented therein negative numbers. And now what about the equation $\sqrt{x}$+1=0, we invent new type of number? For example we ...
3
votes
1answer
192 views

On a scale of 1 to 10, how likely is it that this question is using binary? [closed]

I just read this interesting xkcd strip: At first I thought it was funny, but as I got to ruminate a little over it, I was surprised to be unable to find an answer. As Karolis Juodelė pointed out, ...
0
votes
2answers
70 views

How to convert octal to decimal?

I tried to convert octal to decimal and I found the result but I am expecting different way. My way is: the octal is $547$. Formula: $(5*8^2)+(4*8^1)+(7*8^0)$ Answer: $355$ But I am expecting ...
3
votes
2answers
192 views

History of Calculus

Newton/ Leibniz invented calculus on approximately 1680's. Cauchy/Weierstrauss defined the $\epsilon - \delta$ definition of a limit in approximately 1820's. So how did they define derivatives? I ...
0
votes
1answer
33 views

Conversion Octal to Hexa

How is made the conversion to Hexadecimal by Octal? I know there is a method that is converting to binary and after to octal. There's another? How it works? What is the name of this conversion ...
0
votes
1answer
39 views

How many digits are in the bijective base-k numeral for n?

For integers $n \ge 0$ and $k \ge 2$, the following are equivalent: How many digits are in the bijective base-k numeral for n? If all the words on an alphabet of size $k$ are listed in shortlex ...
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2answers
108 views

Why 5.8 (decimal) is 101.11001100… (binary)?

I would like to know why 5.8, in decimal 101.11001100..., in binary, a recurring decimal?
0
votes
2answers
49 views

Convert HEX to BIN

How to convert the number $fada.cafe_{16}$ to binary? I used Wolfram understand it, but when I type $fada.cafe_{16}$, it changes to $fada.cafdfffffd..._{16}$. Why that?
2
votes
1answer
32 views

Is there an algorithm or method to tell if a fraction can be represented exactly in a particular base?

For instance, 1/3 cannot be represented exactly in base 10, but in many other bases it can. Is there an algorithm that will tell you, given x,y,z, where x and y form a ratio of integers (a fraction) ...
0
votes
1answer
38 views

Combinatorial Number System

I recently read up Combinatorial Number System. I wanted to know how would we find the nth combination when arranged in lexicographic manner and when "repetition was allowed". Eg: {1,2,3} the 6th ...
5
votes
0answers
79 views

A 9 dimensional number system?

Given $x$ and $y$ as sums of nine cubes. When we multiply them, $xy$ may again be written as a sum of nine cubes, due to Wieferich and/or Kempner. Does this invent a 9 dimensional number system, just ...
0
votes
1answer
66 views

How to prove that every number to the power of any other numbers can be express in a+bi?

I was working on some basic complex numbers and suddenly have a question about it. As you all know, the complex numbers are created as we cannot find a place in the real number system to fit in the ...
0
votes
1answer
102 views

Modulus trick in programming

Given two very large integers,assume the length=1,000,000 digits,how will you compute $a^b \mod 10^7$.Since the two numbers are large, of course the value of a^b will be large. So,we find only the ...
1
vote
2answers
53 views

Help with natural number problems

Suppose that $\mathbb{F}$ is an ordered field with identities $0$ and $1^{\star}$ (in this problem, $1 \in \mathbb{N}$ ) Define inductively $f: \mathbb{N} \rightarrow \mathbb{F}$ by: $$f(1) = ...
0
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2answers
57 views

Rational numbers in base 6

Express the fractions , for several small values of , in base 6. Determine which rational numbers have terminating expressions in base 6. I am unsure how to reduce fractions in base 6. For example, ...
2
votes
0answers
41 views

Is 000 (multiple zeros) a valid representation of zero?

I noticed recently that both PHP and Qalculate! (a calculator) accept numbers like 00 or 00000 as meaning 0 (zero). I was curious if these are mathematically valid representations of zero or whether ...
0
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4answers
71 views

Convert 59 to octal

I'm reading Discrete Mathematics by Kevin Ferland and I'm stuck with exercise 33 of Chapter 0: Write the octal number equivalent ...
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3answers
126 views

Converting Base 16 digits to base 2 and 10 - Analysis Question

With base $16$, the digits are denoted as $0, 1,\ldots, 9, A,\ldots, F$. Let $n = AB_3$. Rewrite $n$ with bases $10$, $2$. I have no clue what this question means and how I should attempt to do this. ...
1
vote
1answer
49 views

Determine the number of solutions for $x^2 = c$ such that $c \in \mathbb{F}$

I am working on the problem from number system class taught by the professor who shares his knowledge about the relation of abstract algebra and number systems. Here is the problem: Assume $c$ and ...
11
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2answers
211 views

What mathematical structure models arithmetic with physical units?

In physics we deal with quantities which have a magnitude and a unit type, such as 4m, 9.8 m/s², and so forth. We might represent these as elements of $\Bbb R\times \Bbb Q^n$ (where there are $n$ ...
0
votes
1answer
26 views

Divisibility test for any arbitrary number n

Does there exist any generalised method for devising a test of divisibility for any number. I have found a method and am interested in doing further research in this area. I want confirm whether ...
7
votes
2answers
377 views

Explaining Hypercomplex numbers to Children.

Imagine a highschool freshman walks up to you and asks you what hypercomplex numbers are. Explain to her, in a fair amount of detail, the different types of hypercomplex numbers in a way that any ...
0
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1answer
58 views

Modern Definition of the Real Numbers

I have been told: "The real numbers are defined to be the set of equivalence classes of pairs of rational sequences $(a_i,b_i)$, where (1) $\{a_i\}$ is increasing, (2) $\{b_i\}$ is decreasing, (3) ...