NOR

A NOR gate is trivially made:

Desired Gate	NOR Construction
A B Q 0 0 1 0 1 0 1 0 0 1 1 0

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.

Desired Gate	NOR Construction
A Q 0 1 1 0

OR

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

Desired Gate	NOR Construction
A B Q 0 0 0 0 1 1 1 0 1 1 1 1

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.

Desired Gate	NOR Construction
A B Q 0 0 0 0 1 0 1 0 0 1 1 1

NAND

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

Desired Gate	NOR Construction
A B Q 0 0 1 0 1 1 1 0 1 1 1 0

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.

Desired Gate	NOR Construction
A B Q 0 0 1 0 1 0 1 0 0 1 1 1

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

Desired Gate	NOR Construction

XOR

An XOR gate is made by considering the conjunctive normal form ${\displaystyle (A+B)\cdot ({\overline {A}}+{\overline {B}})}$, 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.

Desired Gate	NOR Construction
A B Q 0 0 0 0 1 1 1 0 1 1 1 0

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.

Desired Gate	NOR Construction