Questions tagged [binary]

For challenges about binary, or the base 2 number system.

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Compact Binary Representation

Background Often, when storing a number in binary with some maximum, we simply round the maximum to the next power of two then allocate the number of bits nececairy to store the whole range. Lets call ...
mousetail's user avatar
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10 votes
6 answers
715 views

Convert from Spoken Binary

This is an exact inverse of the question Convert to Spoken Binary. This introduction is copied from there. Introduction In the video the best way to count, binary is proposed as the best system of ...
Tbw's user avatar
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16 votes
6 answers
1k views

Convert to Spoken Binary

Introduction In the video the best way to count, binary is proposed as the best system of counting numbers. Along with this argument is a proposal on how to say numbers in this system. First, we give ...
Tbw's user avatar
  • 1,119
18 votes
36 answers
2k views

Rudin-Shapiro sequence

The Rudin-Shapiro sequence is a sequence of \$1\$s and \$-1\$s defined as follows: \$r_n = (-1)^{u_n}\$, where \$u_n\$ is the number of occurrences of (possibly overlapping) \$11\$ in the binary ...
alephalpha's user avatar
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2 votes
2 answers
219 views

Binary expansion and partition numbers [closed]

Not sure if it's correct to ask such a question on this site, but let's try. Let a(n) be a sequence of positive integer such that a(1) = 1. To reproduce the sequence a(n) through itself, use the ...
Notamathematician's user avatar
20 votes
23 answers
2k views

Diagonal Binary Sequence

Challenge: Given a positive number \$n\$, convert it to binary, and output a sequence where all 1s form a top-left to bottom-right diagonal line, including a ...
Kevin Cruijssen's user avatar
16 votes
5 answers
655 views

Prefix code generator

In this challenge, we consider an encoding from positive integers (up to a limit) to binary sequences. Some examples: ...
Bubbler's user avatar
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11 votes
35 answers
3k views

Convert binary to unary

The title says it all; Given a number in the binary (base-2) number system, output the same number expressed in unary (base-1). You should take the binary number as a string (optionally with a ...
noodle man's user avatar
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1 vote
1 answer
163 views

Start a program so that /proc/self/cmdline contains a binary representation of the input number

I am sorry for the very long description. But i think some information of how /proc/self/cmdline works and how it can be used to get a integer input was necessary. ...
12431234123412341234123's user avatar
1 vote
0 answers
150 views

making a binary string palindrome using xor operations [closed]

Problem You are given a binary string A of length N. You can perform the following type of operation on the string A: Choose two different indices \$i\$ and \$j\$ (\$1 \le i\$, \$j \le N\$) Change \$...
hemanth's user avatar
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21 votes
13 answers
2k views

Minkowski's ?(x) for rational x

Here is Minkowski's question mark function: It is a strictly increasing and continuous function from the reals to themselves that, among other unusual properties, maps rational numbers to dyadic ...
Parcly Taxel's user avatar
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21 votes
8 answers
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How many xor'ed waves?

In this challenge, you're given a list of overlapping waves. Each wave is a finite list with n truthy values, then n falsy ...
Peter's user avatar
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7 votes
0 answers
221 views

Find the linear transformation

Given a set of bit vectors \$A\$ and a binary matrix \$M\$, we can define the set \$MA = \{ Mx : x \in A \}\$, where \$ M x \$ is the result of the matrix multiplication of \$ M \$ by \$ x \$ over \$\...
Command Master's user avatar
0 votes
0 answers
229 views

How to efficiently count all powers of 2 in a given set of numbers in vb.net?

Every integer can be expressed in powers of 2. You know this as the binary system Assume you are given a set of k numbers (...
aludebe's user avatar
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16 votes
7 answers
1k views

Largest Binary Area

Take the sequence of all natural numbers in binary, (1, 10, 11, ..) then write them vertically beside each-other like this (least significant bit on top; 0s have ...
mousetail's user avatar
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32 votes
75 answers
4k views

Number to Binary

It seems we've managed to go all this time without a plain vanilla Number-To-Binary challenge! Whilst this will inevitably be only one element in many languages, it should put a few esolangs through ...
ATaco's user avatar
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8 votes
3 answers
362 views

Injectively saturate bit strings

It can be easily proven using Hall's marriage theorem that given fixed \$n\$ and \$k<n/2\$, there is an injective (one-to-one) function from all \$n\$-bit strings with \$k\$ ones to \$n\$-bit ...
Parcly Taxel's user avatar
  • 3,717
15 votes
3 answers
562 views

Count the number of disjoint 11 blocks

The task is to count the number of disjoint 11 blocks in a 64-bit word, using the minimum number of straight-line instructions. That is, how many nonoverlapping ...
Falk Hüffner's user avatar
15 votes
21 answers
747 views

CGAC2022 Day 16: Playing with bits, Part 2

Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details. As soon as the Elves get bored with the last week's game, Bin comes up with a new game. The rules are similar, ...
Bubbler's user avatar
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8 votes
3 answers
373 views

Smallest and largest 100-bit square with maximum Hamming weight

Introduction In the binary representation of a \$k-\$bit \$(k>1)\$ square number \$n^2, \$ not all bits can be \$1\$. The maximum number of \$1\$-bits (Hamming weight, \$B\$ for short) is given in ...
Hugo Pfoertner's user avatar
13 votes
14 answers
1k views

CGAC2022 Day 10: Help Santa sort presents!

Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details. Santa likes to sort his presents in a special way. He keeps "uninterleaving" the pile of presents into ...
math scat's user avatar
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19 votes
26 answers
1k views

CGAC2022 Day 9: Playing with bits

Part of Code Golf Advent Calendar 2022 event. See the linked meta post for details. The Elves like playing number games. One day, Bin (a friend of Fen) suggests a new game: given a positive integer <...
Bubbler's user avatar
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4 votes
3 answers
271 views

Intermediate Boolean Algebra Calculator

Background With the success of Simple Boolean Algebra Calculator, I present a more difficult problem. Boolean Algebra concerns representing values with letters and simplifying expressions. The ...
Jacob Creutzfeldt's user avatar
29 votes
20 answers
3k views

Simple Boolean Algebra Calculator

Background Boolean Algebra concerns representing values with letters and simplifying expressions. The following is a chart for the standard notation used: Above is what actual boolean algebra looks ...
Jacob Creutzfeldt's user avatar
29 votes
31 answers
2k views

Generate Parity bits

Given a binary message, and the number of parity bits, generate the associated parity bits. A parity bit is a simple form of error detection. It's generated by counting the number of ...
math scat's user avatar
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12 votes
39 answers
3k views

Hexadecimal -> Binary Art

Take a list of 2-digit hexadecimal numbers as input, and output the binary value, replacing each 1 with an 'X', and each 0 with a space. For example Input = ...
The Thonnu's user avatar
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21 votes
20 answers
2k views

Cut along the lines

In this challenge you will take as input a non-empty list of binary values (these can be booleans or integers on the range 0-1), you should output all the ways to partition the list into non-empty ...
Wheat Wizard's user avatar
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21 votes
11 answers
2k views

Create a nibble shorthand

I recently stumbled across this image on wikimedia commons. It's a little bit of an information overload at first, but after examining it a bit it shows an interesting number system for writing ...
Wheat Wizard's user avatar
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16 votes
11 answers
1k views

Carryless factors

Carryless multiplication is an operation similar to binary long multiplication, but with XOR instead of addition: ...
Rydwolf Programs's user avatar
13 votes
15 answers
2k views

Advanced Binary Number System

Your task is to write a program that calculates the amount of different ways to display any given whole positive number using the following rules: Meet the 'advanced binary system': Any whole positive ...
Squareoot's user avatar
  • 145
13 votes
7 answers
552 views

Encode the systematic binary Varshamov–Tenengolts code

Background Here on CGCC, a commonly seen subgenre is radiation-hardening – writing a program that works even if one character is deleted. A similar problem is studied in the field of coding theory: ...
ais523 - high effort answers's user avatar
15 votes
16 answers
1k views

Implement Binary Exponentiation

Background In programming, there is a recursive algorithm called binary exponentiation, which allows for large integer powers to be calculated in a faster way. Given a non-zero base \$x\$ and a non-...
Aiden Chow's user avatar
16 votes
14 answers
980 views

Number of binary partitions

We all know that any positive integer can be represented as the sum of powers of two. This is how binary representations work. However there's not just one way to do this. The canonical method, ...
Wheat Wizard's user avatar
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24 votes
25 answers
3k views

How far from binary?

Given a decimal integer n as input, output the smallest (in terms of absolute value) decimal integer m such that the absolute ...
Fatalize's user avatar
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17 votes
14 answers
3k views

I want 8 bits for every character!

This is the reverse of this challenge. Given an encoded list of codepoints and the characters used to encode it, you need to decompress it to its original string. For example, given the encoded list <...
naffetS's user avatar
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21 votes
14 answers
3k views

Bitwise XOR of floats

This is different from Floating Point XOR, and more in the spirit of a comment by R.. GitHub STOP HELPING ICE on that challenge, but I thought of this idea independently. Generalized XOR The bitwise ...
Ovinus Real's user avatar
24 votes
17 answers
4k views

Who needs 8 bits for one character?

Given a string and the characters used to encode it, you need to compress the string by only using as many bits as each character needs. You will return the character codes for each character needed ...
naffetS's user avatar
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32 votes
31 answers
3k views

Collatz Encoding

The Collatz Conjecture The famous Collatz Conjecture (which we will assume to be true for the challenge) defines a sequence for each natural number, and hypothesizes that every such sequence will ...
EphraimRuttenberg's user avatar
15 votes
24 answers
2k views

The Binary Eyes

A binary eye is an odd set of digits, with all of its digits except the center one set to 1 or 0, and the center one set to the opposite of the others. Thus, there are two binary eyes for a given odd ...
LWS SWL's user avatar
  • 420
13 votes
17 answers
1k views

The interstice of two binary numbers

Given two integers, compute the two numbers that come from the blending the bits of the binary numbers of equal length(same number of digits, a number with less digits has zeros added), one after the ...
LWS SWL's user avatar
  • 420
20 votes
30 answers
3k 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 ...
Romanp's user avatar
  • 1,357
19 votes
10 answers
2k views

1 bit, 2 bits, 3 bits, …

Given a positive integer \$n\$, your task is to find out the number of partitions \$a_1+a_2+\dots+a_k=n\$ where each \$a_j\$ has exactly \$j\$ bits set. For instance, there are \$6\$ such partitions ...
Arnauld's user avatar
  • 191k
11 votes
33 answers
1k views

Convert the decimal digits of a string's Unicode codepoints to binary, reinterpret as decimal, and take the sum

Yeah... it's confusing. Let me explain it a little better: With a string, get the unicode code points of each letter Let's use "Hello World!". The code ...
12944qwerty's user avatar
1 vote
0 answers
131 views

Binary with 0's only [closed]

The input message consists of ASCII characters The encoded output message consists of blocks of 0 A block is separated from another block by a space Two consecutive blocks are used to produce a series ...
DialFrost's user avatar
  • 5,049
8 votes
14 answers
727 views

Get all binary between a binary string and its reverse

Your Challenge is to take a binary string as input and get all binary numbers between itself and the reverse of its string representation (the reverse may be less than or greater than the original ...
leo-but-not-the-other-guy's user avatar
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^...
pxeger's user avatar
  • 23.5k
17 votes
11 answers
2k views

Binary triangle A141727

Challenge Generate the 2D sequence of bits of A141727. (Allowed I/O methods explained at the bottom.) ...
Bubbler's user avatar
  • 74.9k
14 votes
12 answers
2k views

Nega-Zeckendorf representation

Background Zeckendorf representation is a numeral system where each digit has the value of Fibonacci numbers (1, 2, 3, 5, 8, 13, ...) and no two consecutive digits can be 1. Nega-Zeckendorf ...
Bubbler's user avatar
  • 74.9k
13 votes
9 answers
864 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, -...
caird coinheringaahin g's user avatar
25 votes
14 answers
2k views

Emanresu numbers

My userid is 100664. In binary this is 11000100100111000. An interesting property of this number is that it can be created entirely by concatenating strings which ...
emanresu A's user avatar
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