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

help me in my problem set qs
6. ### 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. ### 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. ### 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. ### 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. ### Help with Space Inversion Symmetry Problem

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

21. ### 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. ### 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...

47. ### 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. ### 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. ### 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. ### 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...