Implementing Logic with Universal Gates

You will redesign any combinational circuit to use exclusively NAND or NOR gates to optimize physical manufacturing costs and space efficiency.

Implementing Logic with Universal Gates

In this lesson, you will learn how to build any digital circuit using only one type of gate, which simplifies physical manufacturing and reduces production costs.

The Power of "Universal" Gates

In your previous designs, you used a mix of AND, OR, NOT, XOR, and other gates. However, from a hardware manufacturing perspective, stocking five different types of gate chips is inefficient and expensive. We prefer to use Universal Gates—specifically the NAND or NOR gate—because they are functionally complete. This means that by cleverly combining just one of these types, you can recreate the logic of any other gate.

Why NAND?

The NAND gate is the industry favorite. To see how it works, look at how we replace standard logic with NAND configurations:

NOT: Connect both inputs of a NAND gate together. NOT(A) becomes NAND(A, A).
AND: A NAND gate followed by a NOT gate. AND(A, B) becomes NAND(NAND(A, B), NAND(A, B)).
OR: A NAND gate where each input is inverted. OR(A, B) becomes NAND(NAND(A, A), NAND(B, B)).

Optimization in Practice

When you design a circuit for a custom processor or an embedded controller, you often start with a logic expression derived from a Karnaugh Map. To implement it using only NAND gates, you follow a two-step transformation:

Replace every AND and OR gate with its NAND equivalent using the substitution rules above.
Use Boolean Algebra (Double Negation law) to cancel out any back-to-back NOT gates that were created, which simplifies the final physical layout.

By using only NAND gates, you can purchase a single "Quad NAND" chip (which contains four gates in one package) and use it to build your entire design. This reduces the number of unique components on your circuit board, saves space, and lowers the cost of the final product.

Key Takeaway: Because NAND and NOR gates are functionally complete, we can replace any complex logic circuit with a single-gate-type implementation, making hardware design more efficient and cost-effective.