What is Parity: Definition and 220 Discussions

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. N

    Engineering Minimum Hamming Distance for Parity Check Matrix

    My answer: Then, if I am not mistaken, the solution made in that video is mostly guessing about which columns combination can be equals to zero and I found 1st, 2nd, and 3rd rows as well as 2nd, 3rd, 4th rows are equals to zero so the minimum hamming distance is 3 since my answer is mostly...
  2. S

    Comp Sci Parity Check Question -- University Level Intro Course: Networking

    What I know: Parity check is used to detect if there are errors when transmitting data by adding redundancy bits to the dataword (data that we want to send) which creates a codeword. Then the receiver checks if the 1's are even or odd and based on that, we know that there was corruption during...
  3. H

    Kramers-Kronig, parity and delta function

    Hi, First of all, I'm not sure to understand what he Kramers-kronig do exactly. It is used to get the Real part of a function using the imaginary part? Then, when asked to add a peak to the parity at ##\omega = -\omega_0##, is ##Im[\epsilon_r(\omega)] = \delta(\omega^2 - \omega_0 ^2)## correct...
  4. guyvsdcsniper

    Using Parity operator for addition/subtraction

    This is for a Quantum Mechanics class but part b of this question seemed like it relied more on math than physics so I think it appropriate to post here. If not, Mods please move to appropriate place. For the ##\Pi xf(\vec r)+x\Pi f(\vec r)=0## I have my answer circled in red on the first...
  5. deme76

    Problem set with 5 proofs involving odd, even, parity, etc.

    help me in my problem set qs
  6. T

    MHB Parity: Show that the sum contains at least one even number.

    Hello, guys! I have a question that need help! A number with 17 digits is chosen and the order of its digits is inverted, forming a new number, These two numbers are then added up. Show that the sum contains at least one even number.
  7. ergospherical

    I Parity selection rules

    I'm confused by the discussion in section §30 (Parity of a state), page 98 of Landau's QM. The functions ##\psi_u## and ##\psi_g## are odd an even states respectively. If ##f## is a true scalar, then it should remain unchanged by inversion of the co-ordinates. Writing ##q' = -q##, then its...
  8. M

    I Parity operator in 2D

    Hello! What is the 2D (acting in spin space) representation of the parity operator. In principle we can make it a diagonal matrix with the right transformation and given that ##P^2=1## the matrix would be diag(1,1) or diag(1,-1). However spin shouldn't change under parity and using that it seems...
  9. W

    B Symmetry of parity: Mistake in the experiment?

    Recently I saw this YouTube video from Veritassium about CPT -Symmetry: In this video an experiment of Prof. Chien-Shiung Wu is presented, which has proven that parity is not symmetric, by observing the emmition of electrons from Co60 atoms with synchronised spin. After thinking about this...
  10. B

    Help with Space Inversion Symmetry Problem

    {a} P = identity Matrix w/ -1 on diagonals {b} eigenvalues = +/- 1
  11. L

    A potential well with 3-fold reflection symmetry

    When we are talking about Bloch's theorem and also the tight-binding approximation, we can use them to help finding eigenstates of a system. However, I am so confused how to apply it in this case (below is my homework) and don't even know how to start it... All I understand about the Bloch's...
  12. L

    A Hamiltonian commutes with a parity operator -- What does that mean?

    If Hamiltonian commutes with a parity operator ##Px=-x## are then all eigenstates even or odd? Is it true always or only in one-dimensional case?
  13. N

    I Parity Eigenstates

    On page 298 of Shankar's 'Principles of Quantum Mechanics' the author makes the statement : ""In an arbitrary ##\Omega## basis, ##\psi(\omega)## need not be even or odd, even if ##| \psi \rangle ## is a parity eigenstate. "" Can anyone show me how this is the case when in the X basis...
  14. mjmnr3

    Why does a symmetric wavefunction imply the angular momentum is even?

    I looked in the instructor solutions, which are given by: But I don't quite understand the solution, so I hope you can help me understand it. First. Why do we even know we are working with wavefunctions with the quantum numbers n,l,m? Don't we only get these quantum numbers if the particles...
  15. M

    I Parity violation potential

    Hello! I read in several papers (e.g. this one) that if we have 2 levels of fixed, opposite parities, which are the eigenstates of a P,T-even Hamiltonian, and we add a perturbing potential which is P-odd, T-even, the matrix element of the new potential between the 2 states of opposite parity...
  16. M

    I Parity violation in nuclei

    Hello! I don't know much about this, so maybe the answer to my questions follows directly from the math of it, but I was wondering if there is an answer providing more physics intuition to this, not just math: Why can a nucleus have an octupole deformation, as a ground state stationary state...
  17. I

    A Predicting the positive parity and zero spin of the Higgs boson?

    Can we predict the positive parity, and zero spin of the Higgs boson from the decay mode: 𝐻 → 𝛾𝛾?
  18. G

    Checking Parity Invariance of the QED Lagrangian

    Hi, I'm trying to check that the QED Lagrangian $$\mathscr{L}=\bar{\psi}\left(i\!\!\not{\!\partial}-m\right)\psi - \frac{1}{4}F^{\mu\nu}F_{\mu\nu} - J^\mu A_\mu$$ is parity invariant, I'm using the general transformations under parity given by $$\psi(x) \rightarrow...
  19. K

    I Parity and Interactions: Misreading or Misunderstanding?

    I read in Greiner Field Quantization that parity only has meaning in interactions. Did I misread or not understand something correctly?
  20. A

    Bubble chamber experiment on a K− beam

    Hello everybody! Let's begin with the spin. Spin of the ##\Lambda## is ##1/2## and of the pion is ##0##: $$ \frac{1}{2} \otimes 0 = \frac{1}{2}$$ Since I know from the homework statement that ##L=1##: $$ \textbf{J} = \textbf{spin} \otimes \textbf{L} = \frac{1}{2} \otimes 1 = \frac{1}{2} \oplus...
  21. F

    A G-parity - where does the minus sign come from?

    Hi all, I have a question on G-parity. I know it's defined as ## G = exp(-i\pi I_{y})C ##, with ##I_y## being the second component of the isospin and ##C## is the C-parity. In other words, the G-parity should be the C-parity followed by a 180° rotation around the second axis of the isospin...
  22. Phylosopher

    B Why does parity give raise to pseudovectors?

    Summary: Why parity have vectors and pseudovectors? why not only vectors? I am reading Griffiths "Introduction to elementary particle physics" Ed.1. The book obviously is an undergraduate introduction.Thus, not much detail is presented, but I cannot get my head around pseudovectors...
  23. M

    Proving Even Parity for this Expression

    My idea was straight forward calculation: $$\begin{align*}\bar { \psi }' ( x' ) \gamma ^ { \mu } \partial _ { \mu }' \psi ( x' ) &= \psi^\dagger\gamma^{0\dagger}\gamma^0\gamma^\mu \partial_\mu'\gamma^0\psi = \bar\psi\underbrace{\gamma^0\gamma^\mu\gamma^0}_{=\gamma^{\mu\dagger}=-\gamma^\mu}...
  24. J

    Initial states ppbar can proceed to npi^0 with parity conserved

    I'm working on some stuff for particle physics and I had a few questions I wanted to ask . Heres the outline of the problem : Establish which initial states of the ppbar system amongst 1^S_0, 3^S_1, 1^P_1, 3^P_0, 3^P_1, 3^P_2, 1^D_2, 3^D_1, 3^D_2, 3^D_3 the reaction ppbar->npi^0 can...
  25. D

    I Parity operator and a free particle on a circle

    Hi. I have just looked at a question concerning a free particle on a circle with ψ(0) = ψ(L). The question asks to find a self-adjoint operator that commutes with H but not p. Because H commutes with p , i assumed there was no such operator. The answer given , was the parity operator. It acts...
  26. renec112

    QM: Issues with parity of spherical harmonics and Heisenberg

    Hi physics forms! I'm practicing to for an Quantum mechanics exam, and i have a problem. 1. Homework Statement I have two problems, but it's all related to the same main task. I have a state for the Hydrogen: ## \Psi = \frac{1}{\sqrt{2}}(\psi_{100} + i \psi_{211})## where ## \psi_{nlm}##...
  27. Mr Davis 97

    I Explanation for parity difference for # of simple graphs

    http://oeis.org/A000088 This is a list that gives the number of simple graphs on n unlabeled vertices. Could someone conversant in graph theory explain why the number of simple graphs on 4 unlabeled vertices, which is 11, is the only one that seems to be odd (nontrivially), while the rest seem...
  28. J

    A How does parity transformation affect Bloch states?

    Hello! I want to know how does a parity transformation affect Bloch states! I always knew that parity takes the position vector to minus itself (in odd number of dimensions), but I have read that it also takes the Bloch wave vector to minus itself but I have not found a satisfactory proof of...
  29. H

    B Questions about parity

    A pair of non-interacting particles can be described by the state vector: \begin{equation} \Psi_{p_1,\sigma_1,p_2,\sigma_1, t_1, T_1, t_2, T_2} \end{equation} Where T is the isospin and t is the 3rd-component. The parity of this state is the product of the intrinsic parities of the two...
  30. Gene Naden

    I Why does a photon have parity -1

    I am wondering what would be an experiment demonstrating that photon parity is -1. It also occurs to me that one might deduce the parity from Maxwell's equations, though that might be a bit of a stretch since they are classical of course. Also, it occurs to me that parity might be assigned a...
  31. Gene Naden

    I Pion decaying to two neutrons demonstrates odd parity

    Does anyone have a reference to a good explanation of this experiment. I am looking at https://quantummechanics.ucsd.edu/ph130a/130_notes/node323.html I am unable to comprehend the reasoning by which it determines the parity of the two neutrons in the final state. Particularly when it says the...
  32. I

    I Vectors in Minkowski space and parity

    It is known that vectors change them sing under the influence of parity when ##(x,z,y)## change into ##(-x,-z,-y)## $$P: y_{i} \rightarrow -y_{i}$$ where ##i=1,2,3## But what about vectors in Minkowski space? Is it true that $$P: y_{\mu} \rightarrow -y_{\mu}$$ where ##\mu=0,1,2,3##. If yes how...
  33. I

    I Parity of theta term of Lagrangian

    I have a very simple question. Let's consider the theta term of Lagrangian: $$L = \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$$ Investigate parity of this term: $$P(G_{\mu \nu}^a)=+G_{\mu \nu}^a$$ $$P( \tilde{G}^{a, \mu \nu} ) =-G_{\mu \nu}^a$$ It is obvious. But what about...
  34. C

    B Is neutrino spin-parity 1/2+ or 1/2-?

    Wikipedia only tells neutrino spin 1/2, but no tell parity sign: positive or negative?
  35. N

    B Tritium, beta decay, spatial parity

    I bought one of those small tritium veils with phosphorus. Read about beta decay, wow what an interesting read! So there was mention when a neutron decays into a proton it emits an electron and an electron anti-neutrino. Also that there is no spatial parity with the physics. What does no...
  36. Diksha17

    I Vector Parity: +1 or -1? Scalar Difference Explained

    Why is a vector's parity +1 and pseudo vector's parity -1 ? While it is the opposite case for scalars.
  37. V

    Parity violation in lambda baryon decay

    Homework Statement In the weak decay of the lambda baryon to a proton and pion, parity is not conserved, allowing for s and p waves in the orbital wave function of the pion-proton system. Using non-relativistic wavefunctions, find the angular distribution of the protons relative to the...
  38. MaxFieg

    I Wu Experiment and Parity Violation

    I have a question concerning the nature of Ms. Wu's experiment confirming parity violation. I'm very familiar with this experiment and its outcomes, but the setup of the experiment itself, alludes me. Wu found that the electron's emitted from the Cobalt-60 atom always went in the direction...
  39. D

    I Proof that parity operator is Hermitian in 3-D

    Hi. I have been looking at the proof that the parity operator is hermitian in 3-D in the QM book by Zettili and I am confused by the following step ∫ d3r φ*(r) ψ(-r) = ∫ d3r φ*(-r) ψ(r) I realize that the variable has been changed from r to -r. In 3-D x,y,z this is achieved by taking the...
  40. nomadreid

    I Antimatter opposite parity to its matter partner?

    A matter-antimatter pair have opposite spins and charges. Is this the same for parity?
  41. V

    A How parity exchanges right handed and left handed spinors

    Reading through David Tong lecture notes on QFT. On pages 94, he shows the action of parity on spinors. See below link: [1]: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf In (4.75) he confirms that parity exchanges right handed and left handed spinors. Or for an arbitrary...
  42. D

    I Commutator of Parity operator and angular momentum

    Hi I have seen an example of commutator of the Parity operator of the x-coordinate , Px and angular momentum in the z-direction Lz calculated as [ Px , Lz ] ψ(x , y) = -2Lz ψ (-x , y) I have tried to calculate the commutator without operating on a wavefunction and just by expanding...
  43. J

    A Parity and time reversal on derivatives and electric field?

    I am trying to learn how parity and time reversal transform the electric field, ##A_\mu## and ##\partial_\mu##. In other words what: what are ##P \partial_\mu P##, ##T \partial_\mu T##, ##T A_\mu T## and ##P A_\mu P##? My first guess was that ##P A_\mu(t,\vec{x}) P = A_\mu(t,-\vec{x})##, ##T...
  44. T

    Even and odd parity detector with active high/low inputs

    Homework Statement Using a single 74x138, build a 3-bit, active-low, odd-parity detector. (Y0-Y7 are selected by "b2 b1 b0" in binary. Also the nibble "0 0 0" is considered even parity) You may use one NOR gate and one NAND gate, with arbitrary fan-in(>1). Label input variables "I2 I1 I0" and...
  45. Incnis Mrsi

    A Chirality of the electromagnetic force on atomic matter

    It’s commonly held that left and right photons interact with matter in exactly the same way, because electromagnetism “conserves parity”. But we know that P-symmetry, in our world, is generally broken. Even according to the Standard Model, when light propagates through some media, it interacts...
  46. M

    A Dirac Spin Exchange Operator

    The spin exchange operator would have the property $$\begin{align*}P\mid \chi_{\uparrow\downarrow} \rangle = \mid\chi_{\downarrow\uparrow} \rangle & &P\mid \chi_{\downarrow\uparrow} \rangle =\mid \chi_{\uparrow\downarrow} \rangle \end{align*}$$ This also implies ##P\mid \chi_{\text{sym.}}...
  47. J

    I Spin and parity of pion decay

    Hi, I'm recently reading Krane's nuclear physics textbook, and in the meson physics chapter there is a section about the spin and parity of pions. He demonstrated a way to find out the parity of the pion by investigating a pion decay(as in the attached images). I think I understand what he's...
  48. M

    EQualityCoin- What type of model is this?

    Hi everyone, I've been working on developing a crypto-currency called eQualityCoin for a while now and hoped someone here might be able to help me "classify" the system in a formal mathematical sense. The system's main feature is a simple rule for how it determines a purchaser's exchange...
  49. P

    Predicting spin and parity of excited states from shell mode

    Homework Statement Consider the following example from a previous exam. We are to predict the spin and parity for F(A=17,Z=9), Florine, in the ground state and the first two excited states using the shell model. Ground state: Neutrons: (1s 1/2)^2 (1p 3/2)^4 (1p 1/2)^2 Protons: (1s 1/2)^2...
  50. I

    Nuclear shell model, spin and parity predictions

    Homework Statement Not exactly a homework problem but I tried to predict the spin and parity of (the ground states of) ##^{89}Sr##,##^{97}Zr## and ##^{137}Ba## using the shell model and my results seem to differ from the tables. Homework Equations Parity ##\pi = (-1)^l## Figure 4 seems to...