The NOR gate
The NOR gate essentially reverses the effect of a normal OR gate so that instead of outputting 1 if either input is 1, it now outputs 1 only if neither input is 1 and zero in all other cases.
The NOR logic gate is distinguished from the OR gate by the circle at the output side of the gate. The Boolean expression is the same as the or expression but with an added overline to represent not or or NOR.
The NAND gate
The NAND gate essentially reverses the effect of a normal AND gate so that instead of outputting 1 if inputs are 1, it now outputs 1 in all cases except where both inputs are 1 when it outputs 0 instead.
The NAND logic gate is distinguished from the AND gate by the circle at the output side of the gate. The Boolean expression is the same as the and expression but with an added overline to represent not and or NAND.
Both NOR and NAND gates may be part of logic circuits you are asked to interpret or draw.
Universal gates
Both NAND and NOR gates are universal gates. This means you can construct any other common gates using only NAND or NOR gates. This has production advantages allowing large quantities of a single type of gate to be mass produced
at lower prices.