Fundamental Digital Electronics/NAND Logic

Logic NAND
NAND gates are one of the two basic logic gates (the other being NOR logic) from which any other logic gates can be built. Due to this property, NAND and NOR gates are sometimes called "universal gates". However, modern 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).

NOT
A NOT gate is made by joining the inputs of a NAND gate. Since a NAND gate is equivalent to an AND gate followed by a NOT gate, joining the inputs of a NAND gate leaves only the NOT part.

AND
An AND gate is made by following a NAND gate with a NOT gate as shown below. This gives a NOT NAND, i.e. AND.

OR
If the truth table for a NAND gate is examined or by applying De Morgan's Laws, it can be seen that if any of the inputs are 0, then the output will be 1. However to be an OR gate, if any input is 1, the output must also be 1. Therefore, if the inputs are inverted, any high input will trigger a high output.

NOR
A NOR gate is simply an OR gate with an inverted output:

XOR
An XOR gate is made by connecting four NAND gates as shown below. This effectively represents the formula: "(A NAND (A NAND B)) NAND (B NAND (A NAND B))".

XNOR
An XNOR gate is simply an XOR gate with an inverted output: