Questions tagged [bit-manipulation]
The bit-manipulation tag has no usage guidance.
78
questions
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0answers
31 views
Efficient bit-level implementation of Boolean polynomials with few variables
A Boolean polynomial in $n$ variables $x_1, \dots, x_n$ is an expression of the form
$$\sum_{\mathbf{s} \in \{0,1\}^n} c_{\mathbf{s}} x_1^{s_1} \cdots x_n^{s_n}, \quad \text{ where } c_s \in \{0,1\} .$...
0
votes
1answer
41 views
Number of subsequence's with same values of bitwise and, or and xor
GeeksForGeeks
We are given an array arr of $n$ element. We need to count number of
non-empty subsequences such that these individual subsequences have
same values of bitwise AND, OR and XOR. For ...
-2
votes
1answer
46 views
What is the reason for this contradiction about the size of the char type?
the size of one char in C is 4 bytes, however to define an 'A' character we use the sum of two values like this expression here:
or in other way i want to say that the char is 4 bytes size, but in ...
1
vote
2answers
53 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 ...
0
votes
2answers
160 views
Complexity of `n & (n - 1)` should be O(1) or O(log n)?
I'm looking at the methods posted in https://www.geeksforgeeks.org/program-to-find-whether-a-no-is-power-of-two/ for checking whether n is a power of 2.
Method 5, ...
1
vote
1answer
34 views
A small question about generating random variable with geometric distribution
I was reading Professor Knuth's Volume 2 (page 136) about generating a geometrically distributed random variable $N$ (with $p$ as the probability of success).
Basically, the idea is to generate a ...
0
votes
1answer
68 views
Shuffling Bits For Uniform Distribution
I am writing a hashing algorithm to be used in the key-value data store. That is for each key the location of the data is determined. The structure of the data store is given a key, a value needs to ...
2
votes
1answer
51 views
Maximize AND on a sequence of XORs
Problem
We are given 2 arrays a and b both of length n. We build a third array ...
3
votes
4answers
2k views
How to find the largest power of two divisor of a given integer?
Given an integer $x$, I need to find the largest power of two $p = 2^n$ that divides $x$ such that the remainder is zero.
When $x$ is zero, the algorithm should return zero. For odd numbers, it should ...
0
votes
1answer
157 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 ...
0
votes
0answers
21 views
What is the order of magnitude of bitwise operations involved in a SHA-256 hash?
Specifically, how many bitwise operations (approximately, could be just order of magnitude) occur each time a Bitcoin ASIC miner performs a SHA-256 hash in typical mining computation, i.e. as it ...
2
votes
1answer
67 views
Compressing a bit string when I know how many 1s and 0s there are
Say I have a 256 bit bit-string, and I know that there are 16 ones and 240 zeros. I know that this bit string can be compressed, because there are only 256 choose 16...
1
vote
1answer
92 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$...
1
vote
1answer
248 views
Must a Turing machine tape be binary?
I once asked why does computer data bits are usually organized on binary (base 2) sets, rather than on unary (base 1) sets, aiming to also understand why its not also ternary (base 3), heptary (base 7)...
1
vote
1answer
47 views
Book CS:APP, using bit set and bit clear
Okay so I'm going through a book CS:APP.
I'm in chapter 2. And problem 2.13 talks about how the Digital Equipment VAX computer used bis (bit set) and bic (bit clear) instead of Boolean operations AND ...
1
vote
1answer
64 views
How can I prove or disprove that the following function is bijection?
For a research project, I tried to prove or disprove that a function called xxhash128_low is a bijection from 64 bit unsigned integer to 64 bit unsigned integer. I have shown that it is sufficient to ...
4
votes
1answer
69 views
Is the following Greedy algorithm to generate Gray Codes always correct?
I recently solved the basic problem of generating a n-bit Gray Code. The solution I used involved building larger-bit Gray Codes from smaller ones recursively (the solution I've seen on most websites)....
1
vote
0answers
61 views
Is it reasonable to assume modern computers can do hardware math with integers up to 2^64?
I was writing up an algorithm that involved knowing the size of integers my hardware can manage without having to resort to software implementations of math operations and the additional computational ...
0
votes
1answer
108 views
How to prove that n&(n-1) and n&(-n) respectively returns and removes the least significant bit?
In a code, I saw someone use:
n&(n-1) to get the least significant bit of n ⇒ 101000 will return 1000
...
3
votes
2answers
91 views
Right most set bit O(log N)
I tried to do the problem Find first set bit in Geeks for Geeks, and this is the code I used.
...
1
vote
1answer
30 views
XOR operation to swap to value without additional variable
I'm breaking my mind to find a good explanation to split two variables with the XOR operation.
The operation is the following:
...
0
votes
0answers
59 views
Efficient triangular decomposition of an integer
Euclidean division is an iterative process
that has been made super-efficient at the CPU level, right?
Its specification is that if I do (q, r) = f(n, d), I get ...
2
votes
1answer
115 views
If the integer representation used is "0 through 4,294,967,295 (2^32 − 1)", so does this mean the register cannot handle negative numbers?
From Wikipedia:
A 32-bit register can store 2^32 different values. The range of integer values that can be stored in 32 bits depends on the integer representation used. With the two most common ...
1
vote
2answers
47 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?
...
0
votes
2answers
175 views
How are bitwise operators used in normalisation of floating-point numbers?
After having spent a significant amount of time googling this topic, I am still struggling to confidently answer the following question:
...
2
votes
3answers
62 views
Determining the number of iterations needed to find the number of bits in an integer
I'm trying to understand the complexity/number of iterations needed to determine the number of bits in an integer.
...
1
vote
1answer
58 views
Is there a name for X when X bitwise OR Y is Y?
I'm wondering if there is a mathematical or computer science term for a number X such that Y | X = Y? For example:
...
1
vote
2answers
38 views
Is there a way to store an arbitrarily big BigInt in a bit sequence, only later to convert it into a standard BigInt structure?
I am trying to imagine a way of encoding a BigInt into a bit stream, so that it is literally just a sequence of bits. Then upon decoding this bit stream, you would generate the standard BigInt sort of ...
0
votes
2answers
680 views
Intelligent use of XOR operator to find missing number
I've come across the following problem on leetcode & tried to solve it with the following code however there seems to be an even better solution that takes advantage of XOR. Leetcode has a ...
0
votes
0answers
29 views
How computer understand to either represent the original bits or two's complement as value?
Important note
I know that this question may seem too simple for you scientists; however, here is the best place that I know to post it.
Question
Suppose we have an ...
2
votes
1answer
25 views
Uniquely identifying bits
Query: Given $m$ unique integers smaller than $2^n$, can we keep at most $k$ the same bits of each number to uniquely identify them?
Is this problem NP-Hard?
For example, given the $4$ unique ...
0
votes
1answer
155 views
Maximum value of $\{ i \land n \mid a \leq i \leq b \}$
I was doing problems in "Leetcode" and found a problem that I could not solve.
Given a non-negative number $n$ and two non-negative numbers $a$ and $b$, consider every number $i$ such that $a \leq i \...
0
votes
3answers
153 views
Minimum number of ways to write a string
Consider the following question
There are K magical pens (numbered 1 through K). You are given strings P1,P2,…,PK (each of which consists of characters from 'a', 'b', …, 't') ; for each valid i, the ...
1
vote
1answer
2k views
ip/tcp packet decoding without wireshark
How can we manually read and interpret packets properly without using wireshark?
Now from the Ethernet header I know that the Destination MAC Address should be at the 5th byte (after converting bits/...
2
votes
2answers
33 views
Data structure for or-lookups over bit-field associations maps
For a mapping between a bit-arrays and values I want cheap lookups using bitwise-or instead of equality.
Slightly more formally, I have a set of associations $k_i \mapsto v_i$ where $k_i \in \mathcal{...
2
votes
1answer
94 views
Prime checking and factorization with just bit cheking
I've read about some methods of prime factorization like here and here. However, I'm wondering: what can we do in prime factorization with just some bit manipulation and without other variables/...
1
vote
2answers
80 views
If XOR of n distinct numbers is ANDed over one of the number, the result would be zero
Say we Have n distinct numbers
x1,x2,....xn
And we xor the result
xoredResult = x1^x2...^xn
And if we AND(&) with one ...
3
votes
2answers
1k views
Minimum XOR for queries
I was asked the following question in an interview.
Given an array $A$ with $n$ integers and an array $B$ with $m$ integers. For each integer $b \in B$ return and integer $a \in A$ such that $a \...
4
votes
1answer
79 views
Evaluating predicate on binary strings
Consider two unknown binary strings $$X = x_{1} x_{2} \dots x_{n^{2}}, \quad Y = y_{1} y_{2} \dots y_{n^{2}}, \quad x_{i}, y_{i} \in \{0, 1\} .$$ We may request a string $Z = z_{1} z_{2} \dots z_{n^{2}...
0
votes
2answers
54 views
Fundamental motivation behind the use of bits and binary representation
This is a naive question, but what makes binary representation special from a theoretical standpoint and from the standpoint of information theory?
If for technical reasons building ternary computers ...
2
votes
1answer
26 views
Names of power-of-two bit operations on bitsets that would not assume any number interpretation
Three commonly used functions when it comes to bit manipulation are :
is_pow2: Checking that an integer is a power-of-two (only one bit is set): $00010000 \...
1
vote
3answers
113 views
Dividing 2 integers with some constraints
This a problem i came across while practicing binary search. Here is the problem:
Given two integers dividend and divisor, divide two integers without using multiplication, division and mod operator.
...
1
vote
1answer
168 views
How to solve Assigment problem on SPOJ? [closed]
Problem Link - Assign .This problem is known as assignment problem.
I read few solutions Here is one and they are trying to solve it using Bit-masking and DP .I tried and thought hard to ...
2
votes
1answer
111 views
find maximum sum of xors
we are given an Array
Array size <= 10^4 .
0 <= A[i] <= 15
We need to partition the array into 4 subsets (each subset can have zero or more elements ). Take xor of each subset and sum ...
1
vote
0answers
44 views
Least computationally expensive bitwise addition
I am familiar with the oft-cited method of bitwise addition using XOR and left shift for the carry, applied recursively. I was wondering if this is the least computationally expensive way to achieve ...
3
votes
1answer
128 views
Is is possible to determine if a given number is xor combination of some numbers?
I have been given a number Y which is ($a$ xor $b$ xor $c$ xor $d$ xor $e$ ) of some numbers ($a$,$b$,$c$,$d$,$e$) and another no X. Now i have to determine if X is a xor combination of ($a$,$b$,$c$,$...
2
votes
1answer
464 views
Can I simplify successive XOR operations?
I'm doing an online programming challenge where successive XOR operations are used (from codewars.com, if you don't want to create an account, here are the instructions).
We have a rectangle of known ...
4
votes
2answers
1k views
Converting a number from N to 0 in binary
Trying to solve this problem since 2 days. Still unable to figure out even a basic approach.
Given a number $N$ in binary ($1$ to $10^5$), we need to convert it to $0$ using only 2 operations. ...
2
votes
2answers
609 views
Find the bitwise AND of a subarray closest to given number
It was a question I was asked in an online assessment for a company.
Please help me in this question-
Given an array, $A$ of size $N$ and an integer $P$ , find the subarray $B = A[i \dots j]$ such ...
0
votes
2answers
217 views
Given matrix, count paths visiting each number exactly once
We are given matrix of size at most $21$ by $21$, each number of the matrix is either $-1$, which means empty element, or integer between $1$ and $21$. Each integer may occure several more times in ...
