Questions tagged [base-conversion]
Conversion of numbers between positional numeral systems. Most common systems are decimal, binary, hexadecimal etc.
172
questions
11
votes
9answers
966 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\$.
...
7
votes
27answers
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\$
...
13
votes
9answers
627 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
3answers
350 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 ...
10
votes
13answers
681 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
15answers
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 ...
5
votes
12answers
912 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 ...
8
votes
17answers
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 ...
25
votes
31answers
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 ...
12
votes
3answers
333 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 ...
22
votes
25answers
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 ...
14
votes
12answers
901 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
25answers
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 ...
21
votes
27answers
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]{...
26
votes
17answers
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 ...
22
votes
36answers
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
7answers
707 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}...
11
votes
8answers
976 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
$$ m \times 10^n $$
...
17
votes
11answers
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
2answers
320 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 ...
13
votes
9answers
428 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 ...
19
votes
22answers
3k 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 ...
9
votes
12answers
367 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.
...
29
votes
43answers
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 ...
16
votes
16answers
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 ...
31
votes
4answers
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
2answers
274 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) ...
44
votes
30answers
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 ...
18
votes
19answers
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 ...
-1
votes
11answers
374 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 ...
-2
votes
11answers
367 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
13answers
539 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
1answer
231 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\$
...
22
votes
26answers
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 ...
0
votes
7answers
621 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 ...
8
votes
5answers
742 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 ...
30
votes
18answers
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
34answers
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
32answers
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 ...
2
votes
2answers
148 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
2answers
203 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
28answers
462 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 ...
27
votes
44answers
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. (...
15
votes
10answers
759 views
Several bases but not twice the same digit
Input
A non-empty array of positive integers.
Task
Convert each integer to either binary, octal, decimal or hexadecimal in such a way that each digit (0 to F) is used at most once.
Output
The ...
12
votes
4answers
549 views
Integers in Base Pi
Background:
Pi (π) is a transcendental number, and therefore it has a non-terminating decimal representation. Similar, the representation doesn't terminate if ...
26
votes
15answers
2k views
Not Quite Roman Ternary
Given an integer n ≥ 0 , output it in a non-positional base-3 notation, using digits 139ABCDE… and a 1-character separator. Every digit is a consecutive power of 3 ...
11
votes
3answers
926 views
Crazy but Rational Bases
We have many challenges based on base 10, base 2, base 36, or even base -10, but what about all the other rational bases?
Task
Given an integer in base 10 and a rational base, return the integer in ...
8
votes
8answers
834 views
Extension of the Game of Sevens
Introduction
Output all the numbers in specific base that would appear in an adapted version of the game of seven.
Challenge
Your task is to output all the numbers in a given base in a given range, ...
11
votes
4answers
467 views
Balanced ternary logic
Balanced ternary logic
Ternary is normally another name for base 3, that is to say, each digit is 0, 1, or ...
24
votes
14answers
1k views
Parse the Parcel
Thanks to your help in the Mark My Mail challenge, PPCG-Post has successfully stamped all of its parcels with the generated barcodes!
Now, it's time to decode them.
In this challenge your program ...
