Universal Gates — Digital Logic -

💡 Logic Gates and Switching Circuits (Universal Gates)

By now, you’ve probably met the three basic gates — AND, OR, and NOT — right?
They’re like the building blocks of all digital circuits.
But there’s a cool shortcut — imagine you could design any logic circuit using just one type of gate.
Wouldn’t that make things simpler?

That’s exactly what universal gates do!
They’re called “universal” because you can create any other logic gate using only them.

🔍 What Are Universal Gates?

A universal gate is a type of logic gate that can perform all basic logic operations — AND, OR, and NOT — all by itself (when used in different combinations).

There are two universal gates:

NAND Gate
NOR Gate

Let’s get to know them one by one.

⚙️ 1️⃣ NAND Gate

The word NAND comes from NOT + AND.
It simply means it does the opposite of an AND gate.

So first, it performs an AND operation, and then it inverts (NOT) the result.

🧩 Truth Table

Input J	Input L	AND Output	NAND Output
0	0	0	1
0	1	0	1
1	0	0	1
1	1	1	0

🧠 How to Think About It

Imagine you have two switches connected in series (like an AND gate) — the light turns ON only when both switches are ON.
Now, flip the rule: the light stays ON until both switches are ON together — then it turns OFF.
That’s how a NAND gate behaves!

🧮 Expression

N = (J · L)’
(read as “NOT (J AND L)”)

⚙️ 2️⃣ NOR Gate

The NOR gate stands for NOT + OR.
So it first performs the OR operation, and then inverts the result.

🧩 Truth Table

Input J	Input L	OR Output	NOR Output
0	0	0	1
0	1	1	0
1	0	1	0
1	1	1	0

🧠 How to Picture It

Imagine two switches connected in parallel (like an OR gate).
The light turns ON if either one of the switches is ON.
Now, reverse that behavior — the light stays ON only when both switches are OFF.
That’s a NOR gate in action.

🧮 Expression

N = (J + L)’
(read as “NOT (J OR L)”)

💪 Why Are NAND and NOR Called “Universal”?

Here’s the interesting part — with just NAND or NOR, you can build any other gate, even the basic ones!

For example, using only NAND gates, you can make:

A NOT gate by connecting both inputs together.
An AND gate by combining multiple NANDs cleverly.
An OR gate through another simple arrangement.

The same trick works with NOR gates too.

It’s like saying:

“If you only had NAND gates in your toolkit, you could still build an entire computer!”

That’s the magic of universal gates.

🧩 Building Other Gates Using NAND

Let’s see how that works:

NOT gate using NAND
Connect both inputs of a NAND gate together.

Input J
Output = (J · J)’ = J’
✅ Works exactly like a NOT gate!

AND gate using NAND
Combine two NAND gates:

First NAND gives (J · L)’
Second NAND inverts it again → ((J · L)’)’ = J · L
✅ You just created an AND gate from NAND gates.

OR gate using NAND
Apply De Morgan’s law:

J + L = (J’ · L’)’
Use NANDs to form J’ and L’, then one more NAND for the final output.
✅ OR gate achieved!

🧩 Building Other Gates Using NOR

Similarly, you can build all gates from NOR gates:

NOT gate using NOR
Connect both inputs together → (J + J)’ = J’
OR gate using NOR
Combine two NOR gates cleverly to invert the result again.
AND gate using NOR
Use De Morgan’s law again → J · L = (J’ + L’)’
Make J’ and L’ using NOR gates, and then one more NOR to finish it off.

🌍 Real-Life Analogy

Think of NAND and NOR gates like the “wildcards” in a card game.
Even if you lose all your other cards (AND, OR, NOT),
you can still play any move you want — just by using these two!

They give flexibility and simplicity in circuit design,
which is why real computer chips often rely heavily on NAND gates — they’re easy to make, fast, and reliable.

⚡ Why Universal Gates Matter

Design Simplicity: You don’t need multiple types of gates — just one universal gate can handle everything.
Practical Use: Most microchips use NAND gates because they’re cheaper and faster to produce.
Foundation of Logic: They show that all logical operations are interconnected — one can be expressed in terms of another.