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Questions tagged [base-conversion]

40 questions
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Base conversion puzzle

Here's an old puzzle: Let $s$ be a string of decimal digits ($s[i] \in \{0,\dotsc, 9\}$). Define a function $f(s)$ as follows: Interpret $s$ as a decimal number, $n_{10}$, and convert $n$ to its octal equivalent, $m_8$. Now treat $m$ as a decimal…
Rick Decker
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How to find a basis which is guaranteed to need 9 or less characters to represent a 12 digits number?

I'm trying to map a 12 digit number into a fixed width file. For a number of reasons, it must be compressed in such a way that it is guaranteed to be less than or equal to 9 characters (alpha numeric is fine). My first thought was a change of…
user34961
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Base transcoding with minimum storage and complexity

I want to reversibly transcode arbitrary information (a digital signature), initially $n$ bits, into symbols in an alphabet with $s$ symbols, with little space loss. In my application‡ $s=45$. Thus I can e.g. transcode $n=192$ bits into $m=\lceil…
fgrieu
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Algorithm to convert decimal number to binary

I am reading this material to understand the basics of number system. I am stuck at a point in that material where it writes the algorithm to convert a decimal number to binary number. The heading of that part where I am stuck is Decimal to Base The…
Ravi
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How does the Bitcoin Algorithm for Converting to Base 58 Work?

I've been trying to create a function in TypeScript for converting to and from base58. I'm pretty familiar with base conversion generally: divide a number by a target base, and take each remainder as a digit of the conversion from right to left,…
devbanana
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Algorithm to convert a fixed-length string to the smallest possible collision-free representation?

I have a US-based telephone number (in the format 000-000-0000) and need to convert it to a "shorter" representation. Using base32/64 produces too long of a string. I've discovered CRC-16, which produces a string of length 4, however, I'm not sure…
anemaria20
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Time complexity of expanding decimal to new base

There is already a post on this topic on stackoverflow. Nevertheless, I am asking the question here again, primarily because I do not understand the answer given there, and also because I have some takes on the problem I would like to supplement…
sss
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4-digit 5's complement of a negative number

Let $n = -13, \ k = -24$ How do I find the 4-digit 5's complement of each number? What would be the result of $n + k$ in complement representation? I understand how to calculate $n$-digit, 2's complement. I convert it to base 2, invert and add…
yarafoudah
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Finding the values of x and y using base 8

In finding the values of x and y, if (x567) + (2yx5) = (71yx) ( all in base 8) I proceeded as under. I assumed x=abc and y=def and followed. (abc+010 def+101 110+abc 111+101)=(111 001 def abc) //adding ()+()=() and equating LHS=RHS. …
tonny
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Are leading zeros necessary when referring to other bases in certain contexts?

I recently took a computer science test where one question was as follows: Each RGB color value can range from _____ to _____ in decimal, _____ to _____ in binary and _____ to _____ in hexadecimal. I answered, Each RGB color value can range from…
Paradox
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Conversion from octal numerical system to binary numerical system

I know that in order to convert a numeral in base-8 to a numeral in base-2 I can write each octal digit as a binary word of 3 bits. I know that 2^3 = 8 that is exactly the dimension of the base of the octal system. I just cannot understand the…
zar
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How to convert between bases partially?

I have some large number $n$ in base $b_1$ and I want to convert it to base $b_2$. $n$ is about a million decimal digits long, therefore it's impractical to convert it as a whole. However I don't need the entire $n$, just some arbitrary slice of it…
jan
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Is there an online algorithm for radix conversion?

Suppose I have $P$, which is the base-$p$ representation of an integer $n$ and I want to calculate it base-$q$ representation $Q$. The obvious algorithm is: interpret $P$ to obtain $n$, then calculate $Q$ from $n$. This is easy. But if $n$ is very…
Mark Dominus
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Shortest decimal expansion within binary interval

Consider an interval $[x-2^n,x+2^n]$ defined by a binary float $x$ and a power of two $2^n$ typically much smaller than $x$. I would like to know whether an efficient algorithm exists to determine the shortest decimal expansion within the interval.…
equaeghe
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