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# Questions tagged [base-conversion]

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

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### 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) of ...
8k views

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 ...
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 ...
215 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 ...
304 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 ...
513 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 ...
221 views

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 $n \geq 0$ ...
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 ...
329 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 ...
465 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 ...
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 ...
2k 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 ...
3k 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 ...
142 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 "...
135 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 forbidden): Input a hexadecimal number Convert to octal Then interpret the digits as if ...
391 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 ...
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. (...
723 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 ...
425 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 ...
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 ...
844 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 ...
817 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, ...
403 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 ...
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 ...
3k views

### Is this a three-digit number ending in one?

Given a nonnegative integer, return whether it is a three digit number ending in one, in any consistent integer base. In other words, the number needs to be represented in base-N, N being an integer ...
3k views

### Mark My Mail! - ASCII Barcodes

4-state barcodes Many postal services (Royal Mail UK, Canada Post, US Mail, etc) use a 4-state barcode to encode information about their mail. Rendered in ASCII, it may look something like this: | ...
2k views

### Find the BCD difference of a number

BCD difference Given an integer n, convert it to BCD (binary-coded decimal) by replacing each decimal digit with its 4-digit binary representation ...
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### Take a byte out of it!

Your task is to, given an unsigned integer n, find the largest number which can be created by removing a single byte (8 consecutive bits) of data. Example Given ...
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### Smallest Zeroless Base

Given a positive integer n, output the smallest base b >= 2 where the representation of n ...
1k views

### The Binary Square Diagonal Sequence

The binary-square-diagonal-sequence is constructed as follows: Take the sequence of positive natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ... Convert each number to ...
770 views

### Smaller-Base Palindromes

For the purpose of this challenge, a smaller-base palindrome (SBP) is a number which is palindromic in a base between 1 and itself (exclusive), and is not a repdigit in the same base. For example, 5 ...
2k views

### How many Lynch-Bell numbers are there?

Challenge Given an integer, n, as input where 36 >= n >= 2, output how many Lynch-Bell numbers there are in base ...
3k views

### Go away! No-1's Here!

I was playing around with some numbers and found a sequence that, of course, is on OEIS. It is A005823: Numbers whose ternary expansion contains no 1's. It goes: a(2n) = 3*a(n)+2 a(2n+1) = 3*a(...
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### The Binary Binary Expansion

Normally, we decompose a number into binary digits by assigning it with powers of 2, with a coefficient of 0 or 1 for each term: ...
530 views

### Count the Palindromes [duplicate]

Given a number n, calculate the amount of bases in the range of [2, n) in which b(n) is a ...
1k views

### Real base conversion

We've had a few challenges for base conversion, but all of them seem to apply to integer values. Let's do it with real numbers! The challenge Inputs: A real positive number x, expressed in base 10. ...
4k views

### All your base 97 are belong to us

Many programming languages are written using solely printable ASCII, tabs and newlines. These 97 characters are then stored in 8-bit bytes (which are actually capable of holding 256 different ...
986 views

### Find the longest rep digit

Your task is to take a positive number as input, n, and output the length of the longest rep-digit representation of n in any base. For example 7 can be represented as any of the following ...
267 views

### Non-integer bases

Description: A non-integer representation of a number uses non-integer numbers as the bases of a positional numbering system. e.g. Using the golden ratio (the irrational number 1 + √5/2 ≈ 1.61803399 ...
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### How to convert HEX2 to RGBA?

The world of art is full of colour, but the world of the network is even fuller than the world of art of diferent colours and it's renderings. That's why we need to know how to convert one type of ...
6k views

### The best base is 10… Let's reach it!

Input: A positive integer n consisting of digits in the range 0-9. Challenge: If d is the highest digit in the integer, assume the base of the number is d+1. E.g. if the integer is 1256 then you ...
4k views

### Those Greedy Romans!

Given a strictly positive integer, return the shortest possible Roman numeral using only the additive rule. Output must consist of zero or more of each of the characters ...
2k views

### Split me in half

You will be given a number x, where 0 <= x <= 2^32 - 1. You should output a list of numbers in decimal, after recursive ...
1k views

### Calculate the binary split sum of a word

Take a string, s containing printable ASCII-characters as input, and output its "binary split sum". Need an explanation? How do you get the binary split sum? We'...
1k views

Convert a hexadecimal number (of any size) into a binary number. Input A POSITIVE hexadecimal number with a 0x in the beginning. A valid input will always match ...
996 views

### Find the polynomial

We know that f is a polynomial with non-negative integer coefficients. Given f(1) and f(1+f(1)) return f. You may output f as a list of coefficients, an ASCII formatted polynomial, or similar. ...
339 views

### Big base, small digits

The J language has a very silly syntax for specifying constants. I want to focus on one cool feature in particular: the ability to write in arbitrary bases. If you write ...
259 views

### Converting rational numbers to an “alien” data format

For a story I'm writing, I needed to convert 101⅐ (101 + 1/7 if that doesn’t show up for you) into base 47. Expressing an integer in some base brings back memories of first learning how to program ...