# Questions tagged [binary]

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

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18 votes
34 answers
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### 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 ...
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2 votes
2 answers
204 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 ...
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 ...
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16 votes
5 answers
597 views

### Prefix code generator

In this challenge, we consider an encoding from positive integers (up to a limit) to binary sequences. Some examples: ...
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11 votes
34 answers
2k 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 ...
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1 vote
1 answer
158 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. ...
1 vote
0 answers
140 views

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0 votes
0 answers
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### 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 ...
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 ...
• 11.8k
31 votes
70 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 ...
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8 votes
3 answers
355 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 ...
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15 votes
3 answers
557 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 ...
• 253
15 votes
21 answers
743 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, ...
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8 votes
3 answers
367 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 ...
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 ...
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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 <...
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4 votes
3 answers
263 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 ...
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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 ...
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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 ...
• 8,543
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 = ...
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21 votes
20 answers
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### 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 ...
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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 ...
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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: ...
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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 ...
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13 votes
7 answers
538 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: ...
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-...
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16 votes
14 answers
969 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, ...
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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 ...
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15 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 <...
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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 ...
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23 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 ...
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32 votes
31 answers
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### 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 ...
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15 votes
24 answers
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### 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 ...
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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 ...
• 420
20 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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19 votes
10 answers
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### 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 ...
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11 votes
33 answers
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### 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 ...
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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 ...
• 5,053
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 ...
17 votes
11 answers
2k views

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25 votes
14 answers
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### 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 ...
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18 votes
14 answers
1k views

### Encode USB packets (part 2)

Inspired by this video by Ben Eater. This challenge forms a pair with Decode USB packets. The USB 2.0 protocol uses, at a low level, a line code called non-return-to-zero encoding (specifically, a ...
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32 votes
19 answers
3k views

### Decode USB packets

Inspired by this video by Ben Eater. This challenge forms a pair with Encode USB packets. The USB 2.0 protocol uses, at a low level, a line code called non-return-to-zero encoding (specifically, a ...
• 23.3k
18 votes
8 answers
2k views

### Sum of set bits from 1 to n

Given an integer $n$ $(n \ge 1)$, return/output the total number of set bits between $1$ and $n$ inclusive. To make the problem more interesting, your solution must run with a time ...
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