Parity function

In Boolean algebra, a parity function is a Boolean function whose value is 1 if and only if the input vector has an odd number of ones. The parity function of two inputs is also known as the XOR function.

The parity function is notable for its role in theoretical investigation of circuit complexity of Boolean functions.

The output of the Parity Function is the Parity bit.

The ${\displaystyle n}$-variable parity function is the Boolean function ${\displaystyle f:\{0,1\}^{n}\to \{0,1\}}$ with the property that ${\displaystyle f(x)=1}$ if and only if the number of ones in the vector ${\displaystyle x\in \{0,1\}^{n}}$ is odd. In other words, ${\displaystyle f}$ is defined as follows:

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