Digital Circuits/NOR Logic

Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. For example, the, Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, contrary to popular belief, integrated circuits are not constructed exclusively from a single type of gate. Instead, EDA tools are used to convert the description of a logical circuit to a netlist of complex gates (standard cells) or transistors (full custom approach).

NOR
A NOR gate is trivially made:

NOT
This is made by joining the inputs of a NOR gate. As a NOR gate is equivalent to an OR gate leading to NOT gate, this automatically sees to the "OR" part of the NOR gate, eliminating it from consideration and leaving only the NOT part.

OR
The OR gate is simply a NOR gate followed by a NOT gate.

AND
An AND gate gives a 1 output when both inputs are 1; a NOR gate gate gives a 1 output only when both inputs are 0. Therefore, an AND gate is made by inverting the inputs to a NOR gate.

NAND
A NAND gate is made using an AND gate in series with a NOT gate:

XNOR
An XNOR gate can be constructed from four NOR gates implementing the expression (A NOR N) NOR (B NOR N) where N = A NOR B. This construction entails a propagation delay three times that of a single NOR gate and uses four gates.

Alternatively, an XNOR gate is made by considering the conjunctive normal form $$(A + \overline{B}) \cdot (\overline{A} + B)$$, noting from de Morgan's Law that a NOR gate is an inverted-input AND gate. This construction uses five gates instead of four.

XOR
An XOR gate is made by considering the conjunctive normal form $$(A + B) \cdot ( \overline A + \overline B )$$, noting from de Morgan's Law that a NOR gate is an inverted-input AND gate. This construction entails a propagation delay three times that of a single NOR gate and uses five gates.

Alternatively, the 4-gate version of the XNOR gate can be used with an inverter. This construction has a propagation delay four times (instead of three times) that of a single NOR gate.