Questions tagged [bit-manipulation]
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58
questions
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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 ...
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2answers
41 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
35 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:
...
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3answers
60 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.
...
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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:
...
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2answers
32 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 ...
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112 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 ...
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27 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 ...
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11 views
L-System coordinate conversion (as opposed to drawing): Extending the Hilbert Space Filling Curve
I have been reading for some time about L-Systems, and specifically the Hilbert Space filling curve. I am interested in writing a function to convert upper-triangular matrix coordinates into an 1-...
2
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1answer
21 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
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1answer
152 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 \...
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3answers
112 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 ...
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1answer
354 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
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1answer
25 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{...
3
votes
1answer
53 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/...
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2answers
48 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
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2answers
570 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 \...
3
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1answer
58 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}...
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37 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 ...
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1answer
22 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): $00010000 \...
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2answers
64 views
Dividing 2 integers with some constraints
This a problem i came across while practicing binary search. Here is the problem:
Given two integers dividend and divisor, divide two integers without using multiplication, division and mod operator.
...
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24 views
Quantization in deep neural networks
I am following this tutorial about quantization in tensorflow.
tutorial 1
tutorial 2
Tutorial 1, describes the quantization formula as:
My question is, if you have 3 floating point values ...
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1answer
100 views
How to solve Assigment problem on SPOJ? [closed]
Problem Link - Assign .This problem is known as assignment problem.
I read few solutions Here is one and they are trying to solve it using Bit-masking and DP .I tried and thought hard to ...
2
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1answer
73 views
find maximum sum of xors
we are given an Array
Array size <= 10^4 .
0 <= A[i] <= 15
We need to partition the array into 4 subsets (each subset can have zero or more elements ). Take xor of each subset and sum ...
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0answers
32 views
Least computationally expensive bitwise addition
I am familiar with the oft-cited method of bitwise addition using XOR and left shift for the carry, applied recursively. I was wondering if this is the least computationally expensive way to achieve ...
3
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1answer
115 views
Is is possible to determine if a given number is xor combination of some numbers?
I have been given a number Y which is ($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
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1answer
287 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
832 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. ...
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2answers
364 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 ...
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2answers
161 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 ...
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0answers
168 views
Count number of pairs of elements in an array whose bitwise OR is equal to a given integer
Given an integer array and an integer $k$, we have to count the number of pairs of elements from the array whose bitwise OR is $k$ in $O(n)$ time complexity. How could this be done?
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If only using bit-shifts can produce a Turing-machine, or if you need more bitwise operations
So you can have One Instruction Set Computers. But typically these instructions have rather complicated underlying implementations.
addition (addleq, add and branch if less than or equal to zero)
...
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2answers
55 views
How “add” could be implemented in only bitshift operations
Typically, add/subtract/multiply/divide are primitive operations in an Instruction Set Architecture (ISA). I am interested to know if they can instead be implemented efficiently using only bitshift ...
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1answer
35 views
What are 'Butterfly Combinations' and why are they called this way?
In some scientific work describing Discrete Fourier Transform-algorithms, such as the well-known Cooley-Tukey algorithm, I came across the term 'Butterfly operations' and 'Butterfly combinations', ...
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2answers
60 views
What kind of operations can we do with bits?
I wonder if there are more things we can do with bits aside from NOT, AND, OR, XOR operations? I got this question from my teacher and I'm not really sure. How about bit shifting ">>"? Could we count ...
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43 views
Find the minimum N such that the sum of beauty of all numbers from 1 to N is at least X
The beauty of a number is defined as follows :-
...
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1answer
111 views
Given a bitstring generate all bitstring with n flipped bits
For an algorithm I need to be able to iterate over all bit strings where $k$ bits are flipped given a bit string with length $n$ and $n \geq k$. For instance let's say I have the bit string $1001$ and ...
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74 views
Find xor sum of all pairs raised to power of 3
We are given array $A$ of $N$ integers each in the range $1 \leq A_i \leq 2^{30}$, that is we can write each integer with at most 30 bits. The target is to compute $\sum_{1\leq i \leq N,1\leq j<i} (...
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18 views
Find $b$-th bit of a number $n$, with sign [closed]
Let $n\in\mathbb{Z}$ and $0\leq b\leq63$, $b\in\mathbb{N}$. Find the $b$-th bit for the number n on it's $64$ bit representation with sign.
and $T$ be the number of test cases.
This is my attempt:
<...
3
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1answer
41 views
How are the prime numbers encoded in Knuth's example of fitting primes into memory cache?
Could somebody please help me understand what is going on here (in plain English)? I think that $(k \mathbin{\&} 63)$ has the effect of modular division. Is that right? How are the primes encoded /...
3
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1answer
72 views
How to distinguish between bits?
I read a post about differences between synchronous and asynchronous transmission modes.
That post has a picture about how bits flows from terminal to computer in async mode.
But how computer can ...
0
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1answer
705 views
Bytes from integer using bitwise operators
So I am extremely confused with using bitwise shifts used to extract the bytes from an integer. I find that if I do something like this...
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2answers
75 views
Easiest way to find y in $x \text{ xor } y = z$ with given $x \text{ and } z$
Let's say we have given two numbers $x, z$, and we need to find another number $y$ such that $x \text{ xor } y = z$. The xor ( exclusive or ) is bitwise operation: xor table
.
I know that this can be ...
0
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1answer
175 views
How to count number of 1s of the first k positions in a bitset (bitmap)?
Input: Given a bitset $b$, which is is an array of 0s and 1s, of length $L$, and a positive integer $k$.
Output: the total number of 1s in the first $k$ position of $b$.
Obviously it can be done in $...
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103 views
Variable bytes (bit arrays) and flipping single bits?
My interest is strictly theoretical at this point, but ultimately applied.
Is there any problem, theoretically, with defining a byte with m bits, and flipping single bits to connote T/F for a given ...
0
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1answer
66 views
Test a bit substring function
How do we test the following function?
bits(bitstring, i, j)
which returns a copy of the substring from i to ...
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68 views
Difference in bit vectors
I have to write an algorithm for a following problem. I have a function that has 2 parameters: an array of 32 bit unsigned whole numbers - bit vectors [ARR] and distance[dist]. We need to find how ...
0
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1answer
38 views
Convert (x + y = z) to propositional logic formula for 8-bit numbers
(Note: this was asked in the cstheory stackexchange, but I was told this is a more appropriate place for it.)
I have three 8-bit 2's-complement numbers (X, Y, and Z). I want to find a propositional ...
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2answers
379 views
Fast searching through bitarray?
I've been thinking for some time but can't figure a way out.
I have big bitarray i.e. 1000+ items of 10_000 bits strings, I'm searching them now linearly. (currently it is stored in one chunk of ...
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195 views
algorithm - maximum pair-wise xor
Given two integers m and n where m < n find the maximum pair-wise xor sum.
The question is how to choose m distinct integers from 1 to n such that using those m numbers yields the maximum pair-wise ...
