Questions tagged [parity]

This tag is for questions relating to "Parity", a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd.

In mathematics, parity is a term we use to express if a given integer is even or odd.

  • The parity of a number depends only on its remainder after dividing by $2$.
  • An even number has parity $0$ because the remainder after dividing by $2$ is $0$, while an odd number has parity $1$ because the remainder after dividing by $2$ is $1$.
  • Parity is often useful for verifying whether an equality is true or false by using the parity rules of arithmetic to see whether both sides have the same parity.
  • In information theory, a parity bit appended to a binary number provides the simplest form of error detecting code.
  • Parity is an important idea in quantum mechanics because the wavefunctions which represent particles can behave in different ways upon transformation of the coordinate system which describes them.

References:

https://en.wikipedia.org/wiki/Parity_(mathematics)

http://mathworld.wolfram.com/Parity.html

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General results on the change of the parity of a number by repeatedly dividing by 2

I know this question may seem open, but I'm a bit interested in figuring out, getting some ideas, or at least getting some sources on how the parity of a number is affected by repeatedly diving it by 2. My question specifically is How many times…
q.Then
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Coset Leaders and Syndromes

This is my Parity check matrix For Coset Leader 100010 Syndrome is 101 Could any one help me with the procedure, since I figured out that adding up both the columns isn't much of help. 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1
user2971393
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A question on parity from book "Mathematics Circles"

Three hockey pucks, A,B, and C, lie on a playing field. A hockey player hits one of them in such a way that it passes between the other too.He does this 25 times. Can he return the three pucks to their starting positions.(THIS IS A PART OF QUESTION…
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Is the sum $2+2+2+2+\dotsb$ even?

I have failed to find a relevant question, so I am posting one. As the question says, is $2+2+2+\dotsb$ even or odd? Or since this "number" is not an integer, it might be undefined. Furthermore, are the following two expressions…
James C
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