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Questions tagged [bit-manipulation]

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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
44 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
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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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2answers
52 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
123 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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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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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: <...
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1answer
53 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 /...
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1answer
84 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 ...
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1answer
1k 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
321 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 ...
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1answer
251 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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120 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 ...
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1answer
81 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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0answers
84 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 ...
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1answer
42 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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503 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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204 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 ...
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1answer
38 views

Difference between CNOT and 2nd bit bitflip

I understand how the outcome of each is supposed to be different, but in matrix form are these gates not the same? The CNOT matrix negates the second bit regardless of the input of the first.
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2answers
658 views

UInt128 - Compute the product of two UInt128's that are each represented by two UInt64's?

I have a struct like this: struct UInt128 { UInt64 s1; UInt64 s2; } In this struct, s1 represents the highest 64-bits ...
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1answer
1k views

Hamming distance and parity

For an Hamming code of $n$ bit there are $k$ bit reserved for the data and $p$ bit for the parity where $p$ is the minimum integer for which the following inequation is satisfied: $$2^p \geqslant p + ...
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40 views

Bridging inductive natural number and bits?

Most popular representation for the natural numbers in type systems is: Inductive nat : Set := | 0 : nat | S : nat -> nat. However, digital computers ...
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53 views

Avoiding overflow when comparing between 16-bit numbers

Let's say I have a 16-bit number system. and let $a, b$ a 16-bit numbers in this system. I know that the numbers I can represent in this system are between $−32,768$ and $32,767$. Let's say I want ...
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1answer
91 views

How to retrieve reset bit in constant time in a bit array

In a game application there is a session id assigned to each player every time they start a new session. Session id's are always unique and there can be billion users of this game. Whenever a user ...
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1answer
368 views

For given set of integers, find and count the pairs with maximum value of bitwise or

Let's say we have given set of integers $A = \{x_1, x_2, x_3, x_4, \dots, x_n\}$, consisting of exactly $n$ values, all of them positive integers. Now the problem is to find the maximum value of ...
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1answer
41 views

How to access the bit at a particular index? [closed]

How do I access the bit at a particular index in a number using shift operator. Say the number is $n$. Let the index be $i (i: 0 \le i < n).$ Rightmost bit is $0$. The only thing I can ...

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