Digital Design: Boolean Operations

Boolean Logic	Operators	Math / Boolean Form	Verilog Code Form
NOT	$\overline{()}$, ~	$z = \overline a$	z = ~a
OR	$+$, |	$z = a + b$	z = a | b
AND	$\cdot$, &	$z = a \cdot b$	z = a & b
NOR	$\overline{(+)}$, ~(|)	$z = \overline{a + b}$	z = ~ (a | b)
NAND	$\overline{(\cdot)}$, ~(&)	$z = \overline{a \cdot b}$	z = ~ (a & b)
XOR	$\oplus$, ^	$z = a \oplus b = (a \cdot \overline b) + (\overline a \cdot b)$	z = a ^ b
XNOR	$\odot$, ~(^)	$z = a \odot b = \overline{a \oplus b} = (\overline a \cdot \overline b) + (a \cdot b)$	z = ~ (a ^ b)