Realization of Logic Gates Using Universal Gates — Digital Logic

🌟 Logic Gates and Switching Circuits (Realization of Logic Gates Using Universal Gates)

When you first learn about logic gates, you meet the basic ones — AND, OR, and NOT.
Then, as you go deeper, you discover two special heroes: the NAND and NOR gates.
These two are called universal gates, and here’s the cool part — with just one type of these gates, you can build any other logic gate in the world!

Let’s take a friendly walk through this idea.

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💡 What Does “Realization Using Universal Gates” Mean?

The word “realization” in digital logic simply means building or implementing something.
So when we say realization of logic gates using universal gates, we mean:

“How can we create basic gates like AND, OR, or NOT using only NAND or only NOR gates?”

It’s like saying — if you only had one kind of tool in your box, could you still build the entire project?
With universal gates, the answer is yes!

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⚙️ Why NAND and NOR Are Called Universal Gates

Both NAND and NOR gates can perform the job of any other logic gate —
AND, OR, NOT, XOR, XNOR — you name it.

That’s why they’re called universal — because they can “universally” replace all other gates.

Let’s see how.

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🧠 Realization Using NAND Gates

We’ll start with the NAND gate, which stands for NOT-AND.

📘 Step 1: Making a NOT Gate from a NAND Gate

If both inputs of a NAND gate are the same (say, J and J), it acts like a NOT gate.

So:
J NAND J = J'

That’s how a single NAND gate can work as a NOT gate.

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📘 Step 2: Making an AND Gate from NAND Gates

Remember, NAND is the opposite of AND.
So if we pass the output of a NAND gate through another NAND gate used as NOT, we get back an AND.

Example:
(J NAND L)' = J AND L

We can build this by connecting two NAND gates —
one for the main operation, and one for the inversion.

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📘 Step 3: Making an OR Gate from NAND Gates

Here’s a neat trick using De Morgan’s law:

J + L = (J' L')'

That means if we first invert both inputs (using NAND as NOT),
and then pass them through another NAND gate,
we’ll get an OR gate.

So with three NAND gates, we can build one OR gate.

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🧩 Summary of NAND Constructions

Target Gate	NAND Realization	Number of NAND Gates Needed
NOT	J NAND J	1
AND	(J NAND L)’	2
OR	(J’ NAND L’)	3

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🧠 Realization Using NOR Gates

Now let’s move to the NOR gate, which stands for NOT-OR.
Like NAND, it can also be used to build all other gates.

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📘 Step 1: Making a NOT Gate from a NOR Gate

If we give the same input to both terminals, the NOR gate works as a NOT gate.

So:
J NOR J = J'

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📘 Step 2: Making an OR Gate from NOR Gates

A NOR gate’s output is the inverse of OR, so if we invert its output, we’ll get an OR gate.

In short:
(J + L)’ = M (NOR gate)
(M)’ = J + L (by adding another NOR as NOT)

So, two NOR gates can make an OR gate.

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📘 Step 3: Making an AND Gate from NOR Gates

Using De Morgan’s law again:
J . L = (J' + L')'

That means if we first invert both inputs (using NOR as NOT)
and then feed them into another NOR gate,
we’ll get an AND gate.

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🧩 Summary of NOR Constructions

Target Gate	NOR Realization	Number of NOR Gates Needed
NOT	J NOR J	1
OR	(J NOR L) NOR (J NOR L)	2
AND	(J’ + L’)’	3

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💬 Quick Analogy: Universal Gates Are Like Swiss Army Knives

Imagine you have a Swiss Army knife — one compact tool that can act as a knife, screwdriver, bottle opener, and more.
In the same way, NAND and NOR are multi-purpose logic tools.
Even if every other gate disappears, you can still build entire circuits using just one of them!

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🌍 Why This Concept Matters

In the real world, engineers love using NAND and NOR gates because:

1. They are cheaper to manufacture.
2. They make circuit designs simpler and faster.
3. They can perform all necessary logical operations.

That’s why in most digital chips, you’ll find tons of NAND or NOR gates doing the work behind the scenes.

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🎯 Quick Recap

• Universal Gates: NAND and NOR.
• NAND Gate Realizations:
• NOT → J NAND J
• AND → (J NAND L)’
• OR → (J’ NAND L’)
• NOR Gate Realizations:
• NOT → J NOR J
• OR → (J NOR L) NOR (J NOR L)
• AND → (J’ + L’)’
• Universal gates simplify digital design and reduce cost.

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