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. 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

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  3. andrex904

    Exploring Parity & Charge Conjugation in Z Boson Decay

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  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

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  6. H

    Definitions of parity conservation

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  7. HanningWu

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

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  8. Icaro Lorran

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

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  9. Coffee_

    The difference between spatial and intrinsic parity

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  10. S

    Does charge conjugation affect parity?

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  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

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  13. A

    Parity problem in Bernstein Vazirani Algorithm

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  14. A

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

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  15. F

    Using nuclear shell model to determine parity and spin

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  16. blue_leaf77

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  17. binbagsss

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  18. binbagsss

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  19. genxium

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  20. D

    Understanding the Parity-Flipping Nature of the Momentum Operator

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  21. A

    Parity operator commutes with second derivative?

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  22. T

    Possible partial waves for photoelectron of nitrogen

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  23. C

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  24. binbagsss

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  25. binbagsss

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  26. J

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  27. T

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  28. M

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  29. T

    Designing a Parity Bit Circuit for Data Transmission

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  30. M

    Parity of Permutations: Understanding Even and Odd Cycles

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  31. S

    NEW Proof that parity operator is hermitean

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  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

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  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

    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

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  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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