Questions tagged [base-conversion]

Conversion of numbers between positional numeral systems. Most common systems are decimal, binary, hexadecimal etc.

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19 votes
25 answers
1k views

Carry-less sum given a base b

Given a list of positive integers \$\mathcal I=I_1,I_2,I_3,...,I_n\$ and a base \$b>1\$ return their "carry-less sum", i.e. represent \$\mathcal I\$ in base \$b\$ and sum digit-by-digit ...
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19 votes
30 answers
2k views

Convert from variable-width Two's Complement to Integer

Take an input, and convert it from Two's Complement notation (binary where the first bit is negated, but the rest are taken as normal) into an integer (in a somewhat standard output form). Input can ...
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25 votes
16 answers
3k views

Convert to base i - 1

Given \$ i = \sqrt{-1} \$, a base-\$ (i - 1) \$ binary number \$ N \$ with \$ n \$ binary digits from \$ d_{0} \$ to \$ d_{n - 1} \$ satisfies the following equation. $$ N = d_{n - 1} (i - 1) ^ {n - 1}...
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12 votes
20 answers
1k views

Convert a string of ASCII characters to base-3 equivalents

Task similar to this one. Take a string of ASCII characters and convert it to base-3 equivalents separated by a space. For example: Hello, world! Should be ...
  • 1,805
12 votes
14 answers
1k views

Lowest integer with no common digits between given bases

Challenge Given a list of bases for positional numeral systems as input, output the lowest positive integer that when represented in those bases they have no common digits. The input list can be ...
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3 votes
11 answers
482 views

Concatenate characters' indexes in the alphabet in the given numeral system

Given a word, get the indexes of each letter in the alphabet. For example: uncopyrightable becomes: ...
17 votes
11 answers
2k views

Write a number in overflowed binary

We all know how binary conversion works: the sequence of bits $$ b_1, b_2, ..., b_{n-1}, b_n $$ encodes the number $$ b_1 \times 2^{n-1} + b_2 \times 2^{n-2} + ... + b_{n-1} \times 2^1 + b_n \times 2^...
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13 votes
9 answers
998 views

Bijective meets mixed base

Background A bijective base \$b\$ numeration, where \$b\$ is a positive integer, is a bijective positional notation that makes use of \$b\$ symbols with associated values of \$1,2,\cdots,b\$. ...
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8 votes
27 answers
2k views

How long is the number in this base?

Given a positive integer \$n\$ and another positive integer \$b\$ (\$1 < b < 36\$), return the number of digits/length of \$n\$ in base \$b\$ ...
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13 votes
9 answers
693 views

Convert to a non-adjacent form

Consider a form of binary where digits can be any of \$1\$, \$0\$ and \$-1\$. We'll still call this "binary" because we convert the digits from base two. For example, $$\begin{align} [1, 0, -...
19 votes
3 answers
378 views

A multiple of n in every base!

In November 2019, Alon Ran published a particularly lovely sequence in the OEIS, A329126: \$a(n)\$ is the lexicographically earliest string of digits which yields a multiple of \$n\$ when read in any ...
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11 votes
13 answers
709 views

'Plane' the numbers in any base!

Inspired by this Numberphile video. What is planing? In order to 'plane' a sequence of digits, you need to: Identify the lengths of the 'runs' (adjacently repeated digits) in the sequence. Non-...
32 votes
15 answers
2k views

Compute the generalised XOR

The goal of this challenge is to generalise the bitwise XOR function to other bases. Given two non-negative integers \$ x \$ and \$ y \$, and another integer \$ b \$ such that \$ b \geq 2 \$, write a ...
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5 votes
12 answers
924 views

Base-ically Guard

Base: part 1 This is part 2, Strongly suggest you go try out the first one if you haven't tried it. Story As one of the solvers, You've managed to get to the door of the base heaven. In front of the ...
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8 votes
17 answers
1k views

Base-ically god

Story The god of base is opening heaven’s gate for mortals to join the base party. You, as one of the believers, want to follow their steps to ascend to heaven. But not everyone can get in. The god ...
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25 votes
33 answers
2k views

Count the trailing zeros

Given two positive integers \$n\$ and \$b\$, such that \$n > 2\$ and \$n > b > 1\$, count the trailing zeros when converting \$n\$ to base \$b\$. Your program should be able to handle any ...
11 votes
3 answers
346 views

Help me count the Omer

During the 49 days between Passover and Pentecost, Jewish liturgy provides four numerical problems that I've here phrased as code golf problems. Input/Arguments These four, in any order, and by any ...
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23 votes
27 answers
2k views

Based Palindromes

A palindromic number, as a refresher, is any number which reads the same forward as backwards. However, what about palindromes in other bases? Input Any integer b ...
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14 votes
12 answers
921 views

Compute the Redwolf Checksum™ of some data

I will preface this by saying that I made this for fun; I have absolutely no formal knowledge on cryptography or error correction. Do not use this algorithm in anything remotely important. I was kind ...
21 votes
25 answers
1k views

Possible binaries sum

This challenge is inspired by the AoC 2020, Day 14 - Part II, created by Eric Wastl and his team, which asks to output the possible binary values from a bitmask. Let's say we've a bitmask like ...
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23 votes
27 answers
2k views

Perfect radicals

Given a positive integer number \$n\$ output its perfect radical. Definition A perfect radical \$r\$ of a positive integer \$n\$ is the lowest integer root of \$n\$ of any index \$i\$: $$r = \sqrt[i]{...
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26 votes
17 answers
3k views

Convert negadecimal to decimal (and back)

Negadecimal, also known as base -10, is a non-standard positional numeral system. Take the number \$1337_{10}\$. In decimal, this has the value one thousand three hundred thirty seven, and can be ...
23 votes
36 answers
2k views

Display the exponent from a binary floating point number as a decimal value

Had my software final exams recently, one of the last questions had me thinking for a while after the exam had finished. Background IEEE754 numbers are according to the below layout The exponent is ...
18 votes
7 answers
718 views

Combinatorial Decomposition

In the body of this challenge, \$\begin{pmatrix}n\\k\end{pmatrix}\$ is used to represent the number of combinations of \$k\$ elements of \$n\$, also written as \$\frac{n!}{k!(n-k)!}\$ or \$n\mathrm{C}...
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11 votes
8 answers
1k views

Scientific notation in Base-16

Input a scientific notation number (base 10), output scientific notation in base 16 (as defined below). Details In scientific notation, all non-zero numbers are written in the form $$ m \times 10^n $$ ...
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17 votes
11 answers
2k views

The Double-Castle Numbers™

Introduction A double-castle number™ is a positive integer number that has a pattern of $$\underbrace{a\cdots a}_{m\text{ }a\text{s}}b\underbrace{a\cdots a}_{m\text{ }a\text{s}}b\underbrace{a\...
10 votes
2 answers
398 views

Inverse of Conway base 13 function in \$\mathbb{Q}\$

(The \$\mathbb{Q}\$ in the title means rational numbers.) Background Conway base 13 function is an example of a strongly Darboux function, a function that takes every real number on any open ...
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13 votes
9 answers
434 views

Minimal Rotate-Right-Double numbers in base n

Task For a given base \$n \ge 3\$, find the smallest positive integer \$m\$, when written in base \$n\$ and rotated right once, equals \$2m\$. The base-\$n\$ representation of \$m\$ cannot have ...
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19 votes
22 answers
4k views

Convert to and from Base 94

The challenge Make 2 programs which convert decimal to and from base 94, or a bidirectional program. Base 94? Base 94 is like any other base, but instead of 0 to 9 and letters, it uses ASCII ...
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9 votes
12 answers
376 views

Does base n have any Rotate-Left-Double numbers?

Task A Rotate-Left-Double number in base \$n\$ is a number \$m\$, when its base-\$n\$ digits are rotated left once, equals \$2m\$. The base-\$n\$ representation of \$m\$ cannot have leading zeros. ...
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29 votes
43 answers
6k views

Convert a 32 bit binary IPv4 address to its quad-dotted notation

Challenge Write a program or function that converts a 32 bit binary number to its quad-dotted decimal notation (often used for representing IPv4) Quad-dotted decimal A quad-dotted decimal is formed ...
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16 votes
16 answers
1k views

Find the length of a number's "base-jumping" path

Consider a positive integer N written in base b. A sequence is generated from this number by finding the largest digit ...
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31 votes
4 answers
4k views

How close are we, really?

Please note: this is a restricted-source challenge — see details below! Each natural number \$n\$ has 10 faces: its decimal representations in bases \$1\$ through to \$10\$. For example, the 10 faces ...
-1 votes
2 answers
276 views

Mirror, Mirror, on the wall. Who's the fairest of them all?

Well, you know it's Snow White, and the evil Queen is at it again. Will Snow White be saved? Will she fall asleep once again? Will the Prince find her? Challenge: Given an arbitrary number (>= 2) ...
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44 votes
30 answers
9k views

French license plates

Sandbox French License Plates French license plates come in a sequential order, following a specific pattern of numbers and letters : AB-012-CD Challenge Write ...
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18 votes
19 answers
2k views

Simplification of numbers

How, you can’t remember the 6 or 7-digit phone number that appeared on the TV screen for a second?! Using the special technique described below, you will turn into a walking phonebook! Obviously, the ...
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-1 votes
11 answers
452 views

Convert alphanumeric (base-36) sentences into hexadecimal (base-16) sentences

I use "sentence" here loosely to mean "any sequence of words separated by spaces" and "words" to mean "sequences of alphanumeric (hexatrigesimal) characters unseparated by spaces". Conversion is from ...
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-2 votes
11 answers
371 views

Convert a number into "bracket" numerals

"Bracket" numerals are a type of 'numerals' I made up once, and thought would be a nice challenge here. Basically, you convert the input number into base 6, and then transliterate the ...
-1 votes
13 answers
543 views

Find how "smooth" a number is based on binary

I haven't been on PP&CG for a while, so I thought I would post something! Your task is to find how "smooth" a natural number is. Your method is to: 1: Convert the number to binary 2: Find the ...
1 vote
1 answer
238 views

Pumping quine radix

Inspired (you don't need to know them for this challenge) by the Pumping Lemma for various languages, I propose the following challenge: choose some basis \$B \geq 2\$ and an integer \$n \geq 0\$ ...
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23 votes
29 answers
2k views

Digital Sumorial

Given an input n, write a program or function that outputs/returns the sum of the digital sums of n for all the bases 1 to ...
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0 votes
7 answers
746 views

convert decimal to duodecimal

The task is to convert a string representing a number in decimal (base 10) representation to duodecimal (base 12). The input is thus a string, the output should be printed. The input number can be ...
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8 votes
5 answers
799 views

Permutation Encoding

Write a program which can encode text to avoid reusing characters, and convert back. Both normal and encoded forms are restricted to a particular character set: the space character ...
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30 votes
18 answers
2k views

Custom Number Base Converter

The powers that be want to be able to quickly convert any number they have into their own number base using any format they would like. Input Your program must accept 3 parameters. Number: The ...
20 votes
34 answers
3k views

Increment base-36 strings

This is a code golf version of a similar question I asked on stack earlier but thought it'd be an interesting puzzle. Given a string of length 10 which represents a base 36 number, increment it by one ...
24 votes
33 answers
4k views

ASCII art uncompression from a base-n number

This is inspired by an 05AB1E answer by Magic Octupus Urn. Given two arguments, a positive integer and a string/list of characters: Translate the number to base-n, where n is the length of the ...
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2 votes
2 answers
150 views

Divide them all [duplicate]

A Math.SE user have a funny game explained as such: Pick a random positive integer X. Add +1, 0, -1 to make it divisible by 3Keep track of how much you've added and subtracted. That is your "...
1 vote
2 answers
211 views

Hexadecimal, octal, binary, oh my! [duplicate]

This is a code golf puzzle: shortest byte count wins. The program should do the following (standard loopholes obviously forbidden): Input a hexadecimal number Convert to octal Then interpret the ...
-10 votes
28 answers
485 views

What are these letters?

So what might be the shortest language for this simple task? Task: You are given an input of type String - the string is a ...
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29 votes
44 answers
3k views

Up go the bits!

Given an integer N perform the following steps: (using 9 as an example). Receive input N. (9) Convert N from base10 to base2. (...
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