Parity Definition and 220 Threads

A parity bit, or check bit, is a bit added to a string of binary code. Parity bits are a simple form of error detecting code. Parity bits are generally applied to the smallest units of a communication protocol, typically 8-bit octets (bytes), although they can also be applied separately to an entire message string of bits.
The parity bit ensures that the total number of 1-bits in the string is even or odd. Accordingly, there are two variants of parity bits: even parity bit and odd parity bit. In the case of even parity, for a given set of bits, the occurrences of bits whose value is 1 are counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number. If the count of 1s in a given set of bits is already even, the parity bit's value is 0. In the case of odd parity, the coding is reversed. For a given set of bits, if the count of bits with a value of 1 is even, the parity bit value is set to 1 making the total count of 1s in the whole set (including the parity bit) an odd number. If the count of bits with a value of 1 is odd, the count is already odd so the parity bit's value is 0. Even parity is a special case of a cyclic redundancy check (CRC), where the 1-bit CRC is generated by the polynomial x+1.
If a bit is present at a point otherwise dedicated to a parity bit but is not used for parity, it may be referred to as a mark parity bit if the parity bit is always 1, or a space parity bit if the bit is always 0. In such cases where the value of the bit is constant, it may be called a stick parity bit even though its function has nothing to do with parity. The function of such bits varies with the system design, but examples of functions for such bits include timing management or identification of a packet as being of data or address significance. If its actual bit value is irrelevant to its function, the bit amounts to a don't-care term.

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  1. e2theipi2026

    MHB Prove this function changes parity.

    Given the prime number sequence p_n and the function f(n) which counts all composite k\le n such that k and k+2 are both composite, prove that f(p_n) changes parity an infinite number of times. Can there be such a proof?
  2. S

    I Symmetry of Hamiltonian and eigenstates

    Suppose we have an electron in a hydrogen atom that satisfies the time-independent Schrodinger equation: $$-\frac{\hbar ^{2}}{2m}\nabla ^{2}\psi - \frac{e^{2}}{4\pi \epsilon_{0}r}\psi = E\psi$$ How can it be that the Hamiltonian is spherically-symmetric when the energy eigenstate isn't? I was...
  3. andrex904

    Exploring Parity & Charge Conjugation in Z Boson Decay

    Considering a Z boson decay into a fermion-antifermion pair. How can i say if the process respect parity and charge conjugation?Thanks
  4. KostasV

    Parity and integration in spherical coordinates

    Hello people! I have ended up to this integral ##\int_{φ=0}^{2π} \int_{θ=0}^π \sin θ \ \cos θ~Y_{00}^*~Y_{00}~dθ \, dφ## while I was solving a problem. I know that in spherical coordinates when ##\vec r → -\vec r## : 1) The magnitude of ##\vec r## does not change : ##r' → r## 2) The angles...
  5. naima

    Wigner function as average value of parity

    I found two definitions of wigner function on space time. the first uses a Fourier transform of ##\rho (q+ y/2,q-y/2)## the second uses the Weyl transformation and parity operator ## exp (i \pi \theta N)## where N is the occupation number operator. Could you give me a link which shows the...
  6. H

    Definitions of parity conservation

    Definition 1: The expectation value of the observable related to the parity operator ##\hat{P}## is constant over time. That is, \frac{d}{dt}\langle P\rangle=0 \int\Psi^*(r)\ \hat{P}\ \Psi(r)\ dr=constant \begin{align}\int\Psi^*(r)\ \Psi(-r)\ dr=constant\end{align} Definition 2: If the...
  7. HanningWu

    How could this,Sigma0 decay into Lambda and gamma, happens?

    I found an article, titled Electromagnetic Decay of the Σ0(1385) to Λγ , in the arXiv telling that the reaction Σ0→Λ+γ can happen through electromagnetic interaction. However, if I examine the conservation of parity. Parity on the left side is even(P(Σ0)=+), but that on the right side is...
  8. Icaro Lorran

    Can the operator Exp[-I*Pi*L_x/h] be faced as parity?

    Homework Statement The problem originally asks to evaluate ##exp(\frac{-i\pi L_x}{h})## in a ket |l,m>. So I am wondering if I can treat the operator as a parity operator or if I really have to expand that exponential, maybe in function of ##L_+## and ##L_-##. 2. The attempt at a solution If...
  9. Coffee_

    The difference between spatial and intrinsic parity

    Can someone explain on the level of Griffiths QM what the difference between those two parities since I'm quite confused here. Some sources use the terms interchangably, some don't. Could anyone provide good definitions for both terms? Spatial parity seems pretty obvious to me to be the...
  10. S

    Does charge conjugation affect parity?

    "Notice that these transformations do not alter the chirality of particles. A left-handed neutrino would be taken by charge conjugation into a left-handed antineutrino, which does not interact in the Standard Model." --https://en.wikipedia.org/wiki/C-symmetry The excerpt above seems to...
  11. Y

    Parity of photon in nuclear transitions

    Let's say we have a transition from ##J^P = \dfrac{1}{2}^+## to something like ##J^P = \dfrac{5}{2}^+##. It radiates a photon with some energy ##E_\gamma##. How does one know the parity of said photon? How does conservation of parity work here?
  12. G

    Parity and total angular momentum

    Hi, I'd like to know how to calculate parity and total angular momentum of nuclei which have even Z and even N and also Z and N are magic numbers, such as 8O8 or 20Ca20 (the number before the element is Z and the after one is N). I don't know how to insert LaTeX formulas. Thank you in andvance
  13. A

    Parity problem in Bernstein Vazirani Algorithm

    I don't understand the following aspect of the parity problem and if someone could please explain it to me, I would be grateful. In the given quantum circuit, the output f(x) is defined to be x.a = x1a1+x2a2+x3a3(mod 2), where a is a fixed |a1a2a3>. For example, if x=|101> and a=|100>, x.a =...
  14. A

    SU(N) symmetry breaking by non-trivial parity.

    I would like to prove the following: Suppose we have the diagonal matrix ##P = diag(1,\ldots,1, -1,\ldots, 1)##, with ##N_+## elements of ##1## and ##N_-## elements of ##-1## such as ##N_+ + N_- = N## and ##N_+, N_- \geq 1##. This matrix is a non trivial parity matrix since it is not...
  15. F

    Using nuclear shell model to determine parity and spin

    Homework Statement Use the shell model to determine the parity and spin assignments for all the stable isotopes of calcium. Homework Equations n/a The Attempt at a Solution The stable isotopes seem to be 40Ca, 42Ca, 43Ca, 44Ca, 46Ca, and 48Ca I believe all of those isotopes except 43Ca are...
  16. blue_leaf77

    Does Commutativity Always Guarantee Shared Eigenkets?

    Let's denote ## \mathbf{p} ## and ## \Pi ## as the momentum and parity operators respectively. It's known that ## \mathbf{p} ## doesn't commute with ## \Pi ##, so they do not share the same set of eigenkets (plane wave doesn't have parity). But I just calculated that ##[\mathbf{p}^2,\Pi] = 0##...
  17. binbagsss

    Possible decay states strong interaction, parity conservation

    The question is for which of the ##1P## meson states - ##1^{1}P_{1}, 1^{3}P_{0},1^{3}P_{1}, 1^{3}P_{2} ## ##D_{s}## states decaying to a ##1S## state is the decay: ##D_{s}**^{+} -> D_{s}^{+}\pi^{0} ## possible? Solution So the strong interaction conserves parity. Parity of meson is given by...
  18. binbagsss

    Parity formulae, orbital angular momentum, mesons

    So a particle has intrinsic parity ##\pm 1 ## . The parity of a system of particles is given by product of intrinsic parities and the result is: ##(-1)^l ## (1). Questions: 1) How does this result follow? and what exactly is ##l## here? so it's the orbital angular momentum, so say a particle...
  19. genxium

    What is the parity inversion of antisymmetric tensor

    First by antisymmetric tensor I mean the "totally antisymmetric tensor" like this: ##\epsilon^{\alpha\beta\gamma\delta} = \left\{ \begin{array}{clcl} +1 \;\; \text{when superscripts form an even permutation of 1,2,3,4} \\ -1 \;\; \text{when superscripts form an odd permutation of 1,2,3,4} \\ 0...
  20. D

    Understanding the Parity-Flipping Nature of the Momentum Operator

    What does it mean when it is said that the momentum operator flips the parity of the function on which it operates ?
  21. A

    Parity operator commutes with second derivative?

    How do I prove that the parity operator Af(x) = f(-x) commutes with the second derivative operator. I am tempted to write: A∂^2f(x)/∂x^2 = ∂^2f(-x)/∂(-x)^2 = ∂^2f(-x)/∂x^2 = ∂^2Af(x)/∂x^2 But that looks to be abuse of notation..
  22. T

    Possible partial waves for photoelectron of nitrogen

    Homework Statement (a) The nitrogen atom has seven electrons. Write down the electronic configuration in the ground state, and the values of parity (Π), spin (S), orbital angular momentum (L), and total angular momentum (J) of the atom. (b) If an extra electron is attached to form the N–...
  23. C

    Why Is Total Parity of Bits Important in Computing?

    Below is the extraction from quantum computer book, but I think my question is related to classical computing; "Now let us generalize from one to multiple qubits. Figure 1.6 shows five notable multiple bit classical gates, the AND, OR, XOR (exclusive-OR ), NAND and NOR gates. An important...
  24. binbagsss

    Decays possible? Parity conservation, bosons, fermions

    1. Homework Statement The question is to determine which decays are possible for: i) ##P^0 ->\prod^+ \prod^-## ii)##P^0 ->\prod^0 \prod^0## Homework Equations where ##J^p = 0^-, 1^- ## respectively for ##\prod^+, \prod^- , \prod^0## and ##P^0## respectively. The Attempt at a Solution For...
  25. binbagsss

    Basic Decay Equations possible? - Parity, symmetry concepts

    The question is to determine which decays are possible for: i) ##P^0## ## ->\prod## ##^+## ## \prod## ##^-## ii)##P^0## ## ->\prod## ##^0## ## \prod## ##^0## where ##J^p = 0^-, 1^- ## respectively for ## \prod## ##^+##, ## \prod## ##^-## , ## \prod## ##^0## and ##P^0## respectively. For...
  26. J

    Spin parity and attractive/repulsive forces

    In most introductory QFT treatments, it's stated early on (and without proof) that particles with even integral spin are always attractive, while those with odd integral spin can be repulsive; sometimes this is even cited as evidence that the graviton must be spin 2 (I think Feynman's...
  27. T

    Parity violation on macroscopic scale

    a question which is bugging me... Yes, I know that parity is violated only by the Weak Interaction, which is very short range. So I would answer "no, there is no P violation on macroscopic scale" However, many macroscopic properties are the results of what happens on the microscopic level. So...
  28. M

    Parity as a kinematic property?

    Weird question, but does anyone have any feelings on whether parity can be classified as a kinematic property? It doesn't scale with energy and so in that sense doesn't seem to be classifiable as a dynamic property, nor do objects interact through it; but parity is of course violated by the...
  29. T

    Designing a Parity Bit Circuit for Data Transmission

    Homework Statement A parity bit will be 0 if the data contains an even number of 1’s and it will be 1 if the data contains an odd number of 1’s. If during transmission a 1 is changed to a 0 or vice versa, then the parity check at the receiver will fail. Determine the parity P for 4–bits of...
  30. M

    Parity of Permutations: Understanding Even and Odd Cycles

    I'm asked to show that a permutation is even if and only if the number of cycles of even length is even. (And also the odd case) I'm having trouble getting started on this proof because the only definitions of parity of a permutation I can find are essentially this theorem. And obviously I...
  31. S

    NEW Proof that parity operator is hermitean

    If the parity operator ##\hat{P}## is hermitian, then: ##\langle \phi | \hat{P} | \psi \rangle = (\langle \psi | \hat{P} | \phi \rangle)^*## Let us see if the above equation is true. The left hand side of the above equation is: ## \langle \phi | \hat{P} | \psi \rangle =...
  32. B

    Parity of a system composed by 2 particles

    I have read that for a system of 2 particles, the total parity is given by: P=P_1 P_2 (-1)^L where - P_1, P_2= insisec parity of particle 1, 2 - L= relative angular moment what's the meaning of "relative angular moment"? Do I have to add the l numbers of the two particles? And what if I...
  33. evinda

    MHB Parity equivalent to the system

    Hello! (Mmm) I have to write a parity that is equivalent to the system:$$\left\{\begin{matrix} x \equiv 1 \pmod 4\\ x \equiv 2 \pmod 3 \end{matrix}\right.$$ That's what I tried: $4,3$ are coprime. We want to find a $c$,such that $x \equiv c \pmod {4 \cdot 3}$ We set $M=4 \cdot 3=12...
  34. bcrowell

    Parity of stress tensor versus stress-energy tensor

    The stress-energy tensor is an actual tensor, i.e., under a spacetime parity transformation it stays the same, which is what a tensor with two indices is supposed to do according to the tensor transformation law. This also makes sense because in the Einstein field equations, the stress-energy...
  35. 1

    Rules of Parity and Charge Conjugation Parity

    I have two related questions to ask relating to statements found in introductory particle physics textbooks. The first is that the "Dirac equation predicts fermions/anti-fermions have opposite intrinsic parity". I have attempted to verify this by applying the parity transformation to free...
  36. P

    Parity conservation and the Field-Strength Tensor‏

    In reexamining chapter 11 of Jackson's Classical Electrodynamics, especially equations 11.148, it seems obvious that in placing the E and B transformation values into the electro-magnetic field-strength tensor one is ignoring the standard rules which do not allow combining polar vectors and...
  37. J

    Parity of inverse trigonometric functions

    When I place the trigonometric functions in the "wolfram google", it informs the parity of the function, so, sin(x), sinh(x) -> odd cos(x), cosh(x) -> even tan(x), tanh(x) -> odd cot(x), coth(x) -> odd sec(x), sech(x) -> even csc(x), csch(x) -> odd arcsin(x), arcsinh(x) -> odd...
  38. S

    Parity Operator and odd potential function.

    Homework Statement This is a university annual exam question: Show that for a potential V (-r)=-V (r) the wave function is either even or odd parity. Homework Equations The Attempt at a Solution We can determine whether a wavefunctions' parity is time independent based on if the...
  39. G

    List of Charge Conjugation and Parity numbers

    Hi everyone, i am just wondering why I cannot find a list of Charge Conjugation and Parity numbers for all the appropriate particles? I mean, I can look online and sift through sources for individual particles (for example, after some research I have found the the photon has a charge...
  40. F

    Two dimensional Square well and parity

    Homework Statement A particle is placed in the potential (a 2 dimensional square well) V(x) = (0 for -a/2 <= x =< a/2 and -a/2 <= y =<a/2, infinity for x>a/2, x<-a/2 and y>a/2, y<-a/2) The hamiltonian commutes with the parity operator P, Pψ(x,y) = ψ(-x,-y) = λψ(x,y), where the eigenvalue λ...
  41. R

    Parity of the decaying particle

    Homework Statement A particle of spin 3/2 decays into a nucleon and pion. Show how the angular distribution in the final state (with spin not measured) can be used to determine the parity of the decaying particle. Homework Equations The parity of a nucleon and a pion is 1 and...
  42. L

    Parity is Discrete Transformation?

    Why parity is discrete transformation? ##Px=-x## ##P\psi(x)=\psi(-x)## when ##x## is continual variable. Could you explain me difference between discrete and continual transformation?
  43. P

    Parity Operations and CPT Theorem

    Hey all, I have a four part question: Homework Statement Let ψ represent a wave function where x,y,z are spatial coordinates and t is time. The particles \pi^{-}, \pi^{0}, \pi^{+} are pions (\pi mesons). The parity inversion operation is represented by The Attempt at a Solution...
  44. P

    What Are the Implications of Parity Operations and CPT Theorem?

    Hey all, I have a four part question: Homework Statement Let ψ represent a wave function where x,y,z are spatial coordinates and t is time. The particles \pi^{-}, \pi^{0}, \pi^{+} are pions (\pi mesons). The parity inversion operation is represented by The Attempt at a Solution...
  45. M

    Horizontal and vertical parity check

    Hello. I need help in detecting error. The question in the attached file is to first fill in the blanks with vertical and horizontal parities. Secondly, it says that there is an error in the circled part. My problem is, how do I find that error and why is there an error? In the second image, I...
  46. D

    What is the intrinsic parity of anti-particles?

    I don't understand how it's possible for the intrinsic parity of any elementary particle to be anything other than one. The parity operator makes the transformation \mathbf{x} \rightarrow -\mathbf{x}, so the only thing about a state that can change after the parity operator is applied to it are...
  47. P

    Rotational exited states spin and parity

    Hi, If you have a even-even nuclei which is deformed, you get a rotational spectrum of 0+,2+,4+,... I don't understand why the parities are positive for even I and why all members of a rotational band must have the same parity. I read about this in Krane's book: an introduction to nuclear...
  48. S

    Why there is parity Symmetry ?

    Greetings, Can someone give a detailed explanation of why the expectation value of z coordinate in the ground state of hydrogen atom is zero due to parity symmetry? In addition how do you represent parity inversion in spherical coordinates and how do spherical harmonics behave under this...
  49. P

    Exploring the Parity Transformation in the Dirac Equation

    Dirac Equation as Example, Dirac Equation: \left(i\gamma^\mu \partial_\mu -m \right)\psi(x)=0 Can I write it in the following way? \left(i\gamma^0 \partial_0- i\gamma^j \partial_j -m \right)\psi^p(t,{\bf -x})=0
  50. I

    What is the role of parity in quantum mechanics?

    Hi, Homework Statement A quantum harmonic oscillator is in a superposition of states(below): \Psi(x,t) = 1/\sqrt{2} (\Psi_{0}(x,t) + \Psi_{1}(x,t) \Psi_{0}(x,t) = \Phi(x) * e^{-iwt/2} and \Psi_{1}(x,t) = \Phi_{1}(x) * e^{-i3wt/2} Show that <x> = C cos(wt) ...Homework Equations Negative...
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