2.10 Universal Gates

All logic expressions consist of various combinations of OR, AND, and INVERT functions and are implemented by use of these three gates. However, with only NAND and NOR gates available, it is possible to produce the other gates, thus NAND and NOR gates are referred to as universal gates.

Part 2.10.1 NAND Gates

NAND gates can be used to implement any Boolean function:

Inverter
AND Gate
OR Gate
NOR Gate

From the diagram above, it is noted that with the presence of NAND gates, we cam produce an Inverter, AND gate, OR gate, and NOR gate. The mathematical proof of the equivalence of three NAND gates to an OR gate is facilitated using De Morgan's theorem.

(A' + B)' = (A')' + (B')' = A + B

Part 2.10.2 NOR Gates

Inverter
AND Gate
OR Gate
NAND Gate

Again for the proof that three NOR gates can be used to represent an AND gate, we use De Morgan's theorem.

(A' + B') = (A)(B')' = AB

Part 2.10.3 Design Rules:

To arrive to a desirable logic circuit, rules are provided to make the design easier. The following diagram provides useful design hints using AND, OR, NAND and NOR gates: