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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Conversion in Number system

Here I provide the image. My question is why is it necessary to have 2 different results of the same problem. Am I doing something wrong. Please Help! Thanks in advance.
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Two conversions to base three yield different results

How are there two different conversion results for the same bases? Am I doing something wrong?
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number of trailing zeroes of factorial raise to power by another factorial

Finding trailing zeroes in any factorial is easy. Every time you pass a multiple of 10 (or something 5 mod 10) you will accumulate another 0 For example 10! has two trailing zeros, one from ...
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51 views

Calculating a Factorial Base Representation

My friend thought of a system in which each number $n$ (I will first restrict my question to positive integers $n$) is represented by a digit string $(d_l,...,d_1)$ as follows $\forall n \in ...
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Absolute and relative error of a binary number?

Given is the following system $A:={ \pm 1.a_1 a_2 a_3 a_4 \cdot 2^e}$, $a_{i}\in \left \{ 0,1 \right \}$, $i\in \left \{ 1,2,3,4 \right \}$, $e\in \left \{ -8,\ldots,8 \right \}$. Find the absolute ...
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About a specific argument purporting to show $0.999\dots = 1.0$.

I have read the proofs about why $0.9999.... = 1$, which are satisfying. But I can't get the following argument out of my head. Defining $0.9999....$ : Lets construct a non-terminating but recurring ...
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Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?

When we decrease the positive denomenator of a ratio (with positive numerator), the value of the ratio increases. The same happens for negative denomenators. But in zero this law is broken. Were there ...
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332 views

Finding a rational number which is simply normal to relatively prime bases

Let $n\ge 2\in\mathbb Z$. Suppose that a base-$n$-decimal $(0.a_1a_2a_3\cdots)_n$ represents $\sum_{k=1}^{\infty}\frac{a_k}{n^k}$ where $a_{i}\in\{0,1,\cdots,n-1\}\ (i=1,2,\cdots)$ is each digit ...
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Can we construct a number system in which **all** (uni-variable) equations can be solved?

$\mathbb{C}$ is nice and safe, in that it's algebraically closed, so we can solve all polynomials in $\mathbb{C}$, but there are still equations that cannot be solved in this set. I'm wondering: ...
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23 views

How to show that for any $n\in\Bbb N\;,n^+=n+1$

Show that for Any $n\in\Bbb N\;,n^+=n+1$ We know for $ n=0 , 0^+=1+0$ for $n\in\Bbb N$ supposing that $n^+=1+n$ then have to show $(n+1)^+=n+1+1=n^++1$
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between 1-2 there comes 1.1,1.2,1.333,1.679,1.999999 etc So what we crossed to get '2' [closed]

If there are infinite numbers between 2 real numbers, then what number we actually cross to get the next number. eg. between 1-2 there comes 1.1,1.2,1.333,1.679,1.999999 etc So what we crossed to get ...
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84 views

Arrange four nine and two symbol to make total of $100$?

Can you arrange four $9$'s and use of at most $2$ math symbols , make the total be $100$? Is this really possible? If it is possible can you help me out?
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73 views

Prove that in any base the number of digits composing the repetitive mantissa of the reciprocal of a prime $p$ never exceeds $p-1$.

I was trying to find bases where the reciprocals of primes have a short repetitive mantissa. Here is what I found: http://imagizer.imageshack.us/a/img835/7738/c7gb.png The bases are on the left. The ...
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3answers
50 views

How do I add multiple binary numbers without using a partial sum?

I know how to add binary numbers but what I normally do is add the first 2 binary numbers and then add the 3rd one to their sum. It is really slow. $$ 111_2 + 111_2 + 111_2 + 111_2 $$ Here is ...
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Name for numbers with a single non-zero digit.

Given a base, is there a name for the numbers (positive or negative) that have only a single non-zero digit? For example: Decimal: 4000, -30, 0.0008 Binary: 1000 Base 5: 300, -0.1 Contrived ...
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46 views

Using Euclid's Algorithm prove..

Using Euclid's Algorithm prove that the fraction $\frac{24n+5}{18n+4}$ is in lowest terms. Is this solution going to be correct as a proof? Thanks for help!
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Interesting Base summation contest math problem

The problem is as follows: Let $N_b=1_b+2_b+\cdots+100_b$ where $b$ is an integer greater than $2$. Compute the number of values of $b$ for which the sum of the squares of the digits of $N_b$ is at ...
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Solving this equation

Question: Solve: $$3^{2x^2}-2\cdot3^{x^2+x+6}+3^{2(x+6)}=0$$ I thought that we can take $a=3^{x^2}$ and $b = 3^{x+6}$. Then equation becomes $a^2-2ab+b^2=0$, which obviously means $a-b=0$. ...
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Which of the following is the highest value?

Question: Find the highest value among $12^9$, $10^{11}$ and $11^{10}$. I have seen problems like this, but they had surds, these are integers. Also, the LCM of $10$, $11$, $9$ $(990)$ is fairly ...
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32 views

Confusing sum of fractions

Question is to find the sum of: $$(\frac{1}{2^2-1})+(\frac{1}{4^2-1})+(\frac{1}{6^2-1})+(\frac{1}{20^2-1})$$ I know that $a^2-b^2=(a+b)(a-b)$, and that with this I can find the LCM to be 1995, ...
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Base-b Representation of an Integer: Why can I make the assumption about number of terms in expansions in uniqueness part?

Base-b Representation of an Integer: Why can I make the assumption about number of terms in expansions in uniqueness part? Reading the book of Koshy I have come across the below theorem. It ...
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Performing mental arithmetic without a base

I'm sure many of you will be aware of the amazing ability for some people to 'see' mathematical calculations as shapes, and to perform mental arithmetic with very little conscious effort, simply by ...
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Problem related to remainder

A polynomial in $x$ leaves a remainder $2$ and $3$ when divided by $x-1$ and $x+1$. What is the remainder, when divided by $x^2-1$ ?
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What would be the problem in mathematics if there are no negative numbers in number line? [closed]

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 ...
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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?
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47 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 ?
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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 ...
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28 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 ...
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379 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 ...
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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: ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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332 views

Finding set of non recurring non terminating decimals

I need to find a set of two Integers P and Q such that ...
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67 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 ...
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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 ...
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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 ...
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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 ...
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109 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 = ...
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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) ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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207 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.
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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 ...