suppose that x and y are bit strings of length n and m is the number of positions where both x and y have 1s. show that w(x y) = w(x) w(y)− 2m.

Answers

Answer 1

A bit string of length refers to a sequence of bits, each of which can be either 0 or 1, that is a fixed length. The total number of possible bit strings of length n is 2^n.

To start, let's define what the function w() represents. The function w(x) returns the Hamming weight of bit string x, which is the number of positions in the string where the bit is 1.

Now, we need to prove that w(x y) = w(x) w(y)− 2m, where x and y are bit strings of length n and m is the number of positions where both x and y have 1s.

First, let's consider the case where x and y have no 1s in common. In this case, m=0 and w(x y) will be equal to the Hamming weight of the concatenated string x y, which is the sum of the Hamming weights of x and y.

This is because there are no positions in which both x and y have 1s, so the number of 1s in x y will be equal to the number of 1s in x plus the number of 1s in y.

Now, let's consider the case where x and y have some 1s in common. In this case, we need to subtract the number of overlapping 1s from the sum of the Hamming weights of x and y, since these overlapping 1s will be double-counted in the concatenated string x y. The number of overlapping 1s is equal to 2m, since each position where both x and y have a 1 will be counted twice in the concatenated string.

Therefore, we can express w(x y) as w(x) + w(y) - 2m, which is equivalent to w(x) w(y) - 2m. This completes the proof.

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Related Questions

Which Principle of Multimedia Learning is Marni following on a slide that has the main points highlighted and clearly visible to the audience?

A.
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B.
Redundancy Principle

C.
Coherence Principle

D.
Signaling Principle

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The Principle of Multimedia Learning is Marni following on a slide that has the main points highlighted and clearly visible to the audience is the Signaling Principle.

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Answers

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See options below

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What's the difference between an exe file and an msi file?

Answers

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MSI files show that the file is a Windows Installer

Explanation:

EXE files are mainly used to indicate that the file is executable

MSI files show that the file is a Windows Installer

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Hope this helped :)

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what epo server task updates the distributed repositories from the master repository if you are not using lazy caching

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What is a replication task?

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Hence, The EPO server task updates the distributed repositories from the master repository if a person is not using lazy caching and this is called replication task.

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Use the drop-down menus to complete the steps to set up cascading deletes between two related tables

Answers

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For example, if a person were to delete any record that is seen or found in the Clients table, a person would also be in the process of deleting any records in regards to the Projects table with that specific Client No.

Hence, The words that can the complete the steps to set up cascading deletes between two related tables are:

Database Tools The Line Connecting the Tables Cascade Delete Related Records.

See full question below

Use the drop-down menus to complete the steps to set up cascading deletes between two related tables.

1. Click the

tab

2. In the Relationships group, click Relationships

3. Double-click

4. In the Edit Relationship dialog box, add a check mark next to

5. Click OK

Done

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Answer: late answer but for the other ppl - Database Tools , The line connecting the tables , and Cascade Delete Related Records.

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On a Windows operating system, the details of the task manager tab should be used to adjust the priority given to a specific program.

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This question involves the creation and use of a spinner to generate random numbers in a game. a gamespinner object represents a spinner with a given number of sectors, all equal in size. the gamespinner class supports the following behaviors.

creating a new spinner with a specified number of sectors
spinning a spinner and reporting the result
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Answers

Using the knowledge in computational language in JAVA it is possible to write a code that generate random numbers in a game

Writting the code in JAVA:

public class GameSpinner {

int spinner;

int num;

int current;

public GameSpinner(int spinner) {

super();

this.spinner = spinner;

this.current = 0;

this.num = 0;

}

public int spin() {

int curr = 1 + (int) (Math.random() * spinner);

if (this.current == 0 || this.num == 0) {

this.current = 1;

this.num = curr;

return curr;

}

if (this.num == curr) {

this.current = this.current + 1;

return curr;

} else {

this.num = curr;

this.current = 1;

return curr;

}

public int currentRun() {

return this.current;

}

GameSpinnerTest.java

public class GameSpinnerTest {

public static void main(String[] args) {

// TODO Auto-generated method stub

GameSpinner g = new GameSpinner(4);