Questions tagged [binary]

For questions about representing numbers in base 2 or performing arithmetic on them.

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2answers
55 views

Can more compression be achieved when data is sorted (in ascending or descending order)?

Let's say I have a file which is exactly 1 MB in size. Contents of file are : 0001001000... upto 128 bytes (128 bytes per line in file). If I sort it in ascending or descending order (using notepad+...
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4answers
79 views

Why does the BOM consist of two bytes instead of one for example in encoding utf-16

Why does the BOM consist of two bytes instead of one for example in encoding utf-16? Information about the order of bytes can be easily saved on just one byte. Is it because it would be good for the ...
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1answer
24 views

Can possiblity of hash collision be "zero" when we hash same file in different formats?

Let's say I have a file A, which is any normal file (pdf, jpeg, mp3 etc.) Now I get the binary dump of file, say another file B{A}. And the hexdump of file say, file H{A}. Now I hash all the three ...
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1answer
25 views

Which is faster "Sorting strings in ascending order" or "Counting the frequency of all strings "?

I have a binary file with lots of 128 bit strings: For Example Line 1. 1000101001000100001111001010..... Line 2. 011010010101001001010..... and many more. I want to sort them in ascending order, and ...
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0answers
14 views

What would be the simplest and quickest way to convert Morse code to "strict" binary?

I'm trying to find a way to easily convert strings of morse code into strings of "strict" binary, in the way that it is described in this answer. Specifically, where: A dot is represented ...
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5answers
257 views

What are some uses of the Thue-Morse sequence in computer science?

Note: I come from a mathematics background. The Thue-Morse sequence $t_n$ is a binary sequence that takes the value $0$ at the positive integer $n$ if the number of $1$s in its binary expansion is ...
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1answer
198 views

For two large (10^6) integers A and B, find the number of set bits in the result of their multiplication

I've recently stumbled upon a problem that I struggle realy hard with ever since. There are two large decimal integers, order of magnitude $10^6$. The task is to find how many bits in the binary ...
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1answer
53 views

What is the nature of the two bits of data held in a computer memory cell?

I hope this question doesn't offend anyone. I start off by saying that I have and always had difficulty understand the language used in computer science so I have to interpret everything into the ...
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1answer
41 views

How to represent $x$ in hexadecimal form where $x=2^n$?

When a value $x$ is a power of $2$, that is, $x = 2^n$ for some nonnegative integer n, we can readily write $x$ in hexadecimal form by remembering that the binary representation of $x$ is simply $1$ ...
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1answer
86 views

Create binary numbers with a described pattern

I am looking for an algorithm that can create binary numbers following certain patterns. Let $n$ be the size; and assume that is a power of 2. Let $E$ be the exponent; $n = 2^E; k = \log n$. The $0, 1$...
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0answers
39 views

Is it possible to find length of sum of two binary numbers without calculating sum?

I'm doing an assignment where I need to multiply two 16 bit numbers and store result as an 16 bit integer array. a is binary with length of ...
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2answers
49 views

Why is the time complexity of the Bit Manipulation solution to Binary Addition O(M + N)?

I am trying to understand why the time complexity of the Bit Manipulation solution (https://leetcode.com/problems/add-binary/solution/) to the Binary Addition problem is O(M + N), where M and N are ...
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1answer
46 views

is duality principle in boolean algebra is true for every expression

Let say A = 1 and B = 1 and then A+B = 1 now by using duality(replacing or gate by and gate and 1 by 0) we can say that, A.B = 0 but this is not 0, because 1.1 = 1, so please anyone clear my ...
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7answers
19k views

Why does the formula 2n + 1 find the child node in a binary heap?

I learned that when you have a binary heap represented as a vector / list / array with indicies [0, 1, 2, 3, 4, 5, 6, 7, 8, ...] the indicies of the children of element at index n can be found with $...
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1answer
49 views

XOR of three integers where each pair's XOR is the other integer

I have three positive integers, a, b, and c. I know that $a\oplus b\oplus c=0$, so I got that each pairwise xor has to be the other positive integer. $a\oplus b=c$, $b\oplus c=a$, and so on, but I can'...
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1answer
48 views

Changing binary counter structure such that increament and decreament methods will work in O(1) amortized

Just trying to solve the second part of a question with two parts. First part was to prove that you can't add decrement method to a standart binary counter without hurting the amortized complexity and ...
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2answers
73 views

How come the set of all binary strings is uncountable?

Sorry for bumping this very old problem which already has answers on multiple SE sites, but I just cannot understand any of the answers. Let $\Sigma_{bool} = \{0, 1\}$. Then, $(\Sigma_{bool})^*$ is ...
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1answer
38 views

Where is the theory about "binary toggling games"?

Let us -- using parameters $M, N$ and $L$ -- create an ordered set of size $M$ of $N$-bit long vectors $V$ and initialize them randomly: $V_k[i] = b \sim Bin(n=1, p=0.5)\ \forall i \in \{0\ ..\ N-1\}...
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1answer
31 views

How can I tell if a bit pattern can represent offset gray-code?

I have a very poor understanding of gray code in general and I find it to be a difficult thing to learn. While trying to learn about it I stumbled upon this seemingly looking trivial question that I ...
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0answers
20 views

Computing with Extra States

So, computing largely operates through states of 0 or 1, this I am aware of. But I do have a question, is there a meaningful difference in computing using more states. For example, 0, 1, and 2. ...
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0answers
37 views

Efficient method for finding 1's in binary representations

Say I have a binary number of N bits, and I need to find every combination that have M 1's. For example, if N = 3 and M = 1, then 100, 010, 001 are the allowed combinations. I have read that a more ...
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2answers
62 views

Half precision floating point question -- smallest non-zero number

There's a floating point question that popped up and I'm confused about the solution. It states that IEEE 754-2008 introduces half precision, which is a binary floating-point representation that uses ...
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1answer
38 views

How to perform AND on binary "recursive repeating sequences"?

Suppose, we have a two binary sequences, encoded as "recursive repeating sequences" (I don't know exactly how to name them). Each sequence can contain other sequences and has number related ...
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2answers
37 views

Why are binary numbers sometimes written with one or more leading zeros that don't change the number (quantity) represented?

Binary numbers like '0110', or '00100101' are seen very often in all contexts. What are the leading (left hand side) zeroes for? Why did the writer not write '110' and '100101', respectively?
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1answer
51 views

while loop for bitwise conversion program

int counter(char c){ int count = 0; while (c!=0){ if((c & 1) !=0) count++; c = c >> 1; } } I am trying to understand a ...
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3answers
53 views

Negative Numbers in 32 bit Floating Point IEEE Numbers

So I understand the logic behind converting positive decimal numbers to IEEE 32 bit floating numbers but I'm not completely sure behind the negative one's. If for example we have a decimal number say -...
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0answers
44 views

Optimize binary multivariate polynomial multiplication

You have a few variables that can only assume the values 0 or 1 and you use those to form two polynomials. Is there a way to multiply the two polynomials that is faster than O(n²) where n is the ...
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0answers
11 views

About the paper Privacy-preserving in association rule mining using an improved discrete binary artificial bee colony

I don't understand two parts in this paper: The min notion on page 4 line 357 (equation 10d): I understand this as to find all the $M_{10}$, $M_{11}$, $M_{01}$ first and then try to minimize the ...
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4answers
83 views

Is there a binary representation where the encoding distance grows with the arithmetic distance?

I need to binarily encode/decode small integers (around 10 bits), in such a way that the hamming distance of the encoded number grows monotonically with the (absolute value) arithmetic distance of the ...
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1answer
55 views

Assign few binary variables to make all polynomials identically zero

I have 50 polynomials $f_i$ over binary variables $(x_1,\ldots,x_{100})$. Also $f_i(0,0,\ldots,0)=0$ for any $i \in [1,50]$. I want to assign few variables so that all $f_i$ will be identically zero. ...
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2answers
158 views

How do computers *really* work? (at the most basic level)

While learning about computers I will read about RAM and Storage and the CPU, and while these explain the architecture of a computer and how parts of a computer work together, I still don't understand ...
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1answer
137 views

How can you represent a Huffman-tree in Hex?

I was trying to store a Huffman tree in a binary file recently. I thought it wouldn't be a big problem since you actually have the binary codes already in front of you. Well, the difference is that ...
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1answer
22 views

2's complement substraction

I need to perform 2's complement operations on -50 - -48 From a mathematical point of view the following would be true. -50 + 48 = -2 If I would follow the steps I would have: I got to this result by ...
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1answer
28 views

Where does the decimal to binary "Divide by 2" algorithm come from?

I don't know if this board would be an appropriate place for this question, but I have been trying to figure out how the divide-by-2 decimal to binary conversion trick works: in which you divide the ...
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0answers
18 views

Binary 2's complement to decimal

I need to transform 2's complement from binary to decimal The binary integer is 10001001 This is my thought process. Could someone validate my thought process or correct it, please? ...
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1answer
65 views

Consider 4 positive integers a,b,c,d having exactly 10^11 bits (considering the leading zeroes) in the binary representations

Consider 4 positive integers a,b,c,d having exactly 10^11 bits (considering the leading zeroes) in the binary representations. Positions are numbered from 1 to 10^11. Every 3rd bit of a is equal to 1 ...
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1answer
134 views

Greedy algorithm for subset sum on powers of 2

I have some $n$ numbers which are powers of $2$, say $a_1,a_2,a_3,\ldots,a_n$ which are not necessarily all distinct. I have option to give them any sign. I have to find if I can make their sum after ...
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3answers
142 views

Name of binary encoding scheme for integer numbers

I once found on Wikipedia a nice technique for encoding $k \in (2^{n-1}, 2^n)$ uniformly distributed integer numbers with less then $\log_2n$ average bits/symbol, thanks to a simple to compute ...
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1answer
52 views

Probability of loss using a binary symmetric channel

Today we talked about Information Theory and the binary symetric channel. For newbies here is a little explanation : For instance if I want to send a binary to someone : The bit will be "flipped&...
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0answers
39 views

How did we go from Binary to something like Python?

If there's one thing the pandemic has shown us its that High school Geometry did not save us. I am a high school math teacher and I understand my job and its usefulness only exist in a post scarcity ...
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2answers
44 views

Simple question about signed integer multiplication

If you have a signed integer int x = any And then state that x < 0 Is the following statement true or false? ...
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1answer
227 views

Converting Decimal Numbers between 0 and 1 to Binary

I've been playing around with a program I wrote that converts decimal numbers to binary numbers and i've noticed that eventually, after applying the algorithm (multiply by 2, subtract 1 if greater ...
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2answers
59 views

Is a file a string of zeros and ones?

Is a computer file just a string of zeroes and ones? If so, can it start with zeroes? I have not been able to find an answer, surprisingly.
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1answer
18 views

Conversion of fractional part of a hexadecimal number to binary

The Number is given as : (C012.25)Hexadecimal I have to convert it into octal . So I converted it into Binary First and got the result as : 1100000000010010.01000000 (Since each bit in hexadecimal ...
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1answer
43 views

2d cellular automata Wolfram binary codes

This is a similar question to How 2d cellular automata rules works? However, the answer there did not provide me what I am looking for. Specifically, I want to be able to render these 2d cellular ...
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1answer
107 views

How does computer memory store the file name?

I have this doubt for long time. When i save a notepad file, it takes the memory for the information in the file. let's say, I type 'ABC' in notepad and saved the filename as stack, it shows that the ...
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1answer
50 views

How does malware enter the computer and take control on a binary or machine code level?

Malware can enter a computer in various ways, but I would like to know how it is able to simply use 0's and 1's and machine code to take over a computer and how it can stay hidden from antivirus ...
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2answers
923 views

Binary subtraction with numbers in 2's complement

How can i perform binary subtraction of two numbers that are already in 2's complement? I have to subtract 01010011 from 10100110,both numbers are in 2's complement. I know that 10100110 is -90,and ...
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1answer
42 views

Does a megabyte represent (2^8)^1000000 bits in base2? Isn't that more than enough combinations to represent everything?

Every introductory CompSci resource I can find goes through how 8 bits are in a byte, etc. So a byte can store some 2^8 values in binary. Then when asking about four bytes, we can assume this is (2^8)^...
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0answers
41 views

CNF encoding of additions

I have $m$ equations of the following form: $$x_1+x_2+\cdots+x_n=s,$$ where each variable is either 1 or 0, and the total number of variables is $m\approx3{,}000$. So I’m thinking of modeling each ...