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ParityParity is a concept of equality of status or functional equivalence. It has several different specific definitions.
Parity in algebra
The parity of permutations (as defined in abstract algebra) is the parity (even or odd) of the number of transpositions into which the permutation can be decomposed. For example (ABC) to (BCA) is even because it can be done by swapping A and B then C and A (two transpositions).
It can be shown that no permutation can be decomposed both in an even and in an odd number of transpositions. Hence the above is a suitable definition.
Parity in quantum mechanics
Particles have a quantum mechanical property of parity. According to quantum mechanics, the conservation of this parity is equivalent to the laws of physics being invariant under mirror reflection. It has been found that parity is not conserved in the weak force and so the weak force is not invariant under mirror reflection.
See: Parity transformation, P-symmetry, intrinsic parity.
Parity in telecommunications
In this usage, the number of '1' bits in the binary value is counted. Parity is even if there are an even number of '1' bits, and odd otherwise. Examples: the parity of the value 10111101 is even (there are 6 '1' bits); the parity of the value 01110011 is odd (there are 5 '1' bits).
Parity is sometimes used for error checking due to the fact that it may be calculated easily, however much-more robust error checking methods exist!
There are several types of parity: none, marking, even, and odd. 'None' means there is no parity calculated and a zero-bit is usually inserted (that is, the bit is present but unused or ignored). 'Marking' means that the parity bit is always a '1'. 'Even' and 'odd' parity insert '1' or '0' parity bits so that the total number of '1' is even or odd, including the parity bit. The parity bit is 'stripped off' before the data is used, thus a seven-bit character (or data value) requires eight bits to transmit or store - the seven data bits and the parity bit.
Modern error-checking algorithms use CRC or error correcting codes, for example. These codes are more powerful and can often correct errors, while parity can only detect some errors.
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