🧩 Quick Recap First!

Before we dive in, let’s remind ourselves:

• The CPU is the part of the computer that follows instructions.

• It follows these instructions using the Fetch → Decode → Execute cycle.

• Inside the CPU are tiny parts called registers, an ALU (Arithmetic Logic Unit), and a control unit.

• The CPU works one tick at a time — billions of ticks every second!

Now, let’s talk about how this little brain does math — using nothing but switches!

🔌 What Do We Mean by “Switches”?

A switch is just something that can be on (1) or off (0). You can think of it like:

• A light switch: ON = 1, OFF = 0

• A button: Pressed = 1, Not pressed = 0

• Electricity flowing = 1, No electricity = 0

That’s it. Nothing fancy.

Now imagine this: If we connect lots of tiny switches together, we can build machines that add numbers, subtract, and even multiply.

Let’s see how.

➕ Step 1: How to Add Two Bits

Let’s start really small.

What’s a bit again?

A bit is just one switch. It can be:

• 0 (off)

• 1 (on)

Let’s try adding two bits together:

Wait! What’s “10” doing there?

Let’s explain…

🔄 What Happens When 1 + 1 = 10?

Remember: Computers count in binary (just 0s and 1s).
In binary:

• 0 + 1 = 1

• 1 + 0 = 1

• 1 + 1 = 2 → which is 10 in binary.

So, when we add 1 + 1 in the CPU, the answer is:

• 0 on the bottom

• And a carry of 1 to the next column.

Just like how we carry in normal math:

This is the start of something called a half-adder.

🔀 What’s a Full-Adder?

A full-adder adds:

• One bit

• Another bit

• And a carry bit from before

It gives you:

• A new sum bit

• And a new carry bit

This is how CPUs add big numbers — by lining up lots of full-adders, side by side!

🧠 Let’s Add Two 4-Bit Numbers

Let’s say we want to add:

• 0101 (which is 5 in decimal)

• 0011 (which is 3 in decimal)

We feed them into 4 full-adders like this:

   0101
+ 0011
 ———-
   1000

5 + 3 = 8!
That’s 1000 in binary.

Cool, right?

🧮 What Part of the CPU Does This?

This job is handled by the ALU — the Arithmetic Logic Unit.

It’s like the calculator inside your CPU.

• It takes in two binary numbers

• It runs them through the adders

• It gives you a result — fast

No fingers. No calculator. Just switches!

➖ What About Subtraction?

Subtracting is just like adding — but with a little trick.

Let’s say we want to do:

5 – 3 = 2

In binary:

• 5 = 0101

• 3 = 0011

The CPU uses a special math trick called “two’s complement” to turn subtraction into addition.

It’s like saying:

5 + (-3) = 2

So instead of building a new subtractor, the CPU just uses the same adder to do both jobs.

Smart!

🧮 How Big Can CPUs Add?

Early computers could only add 8-bit numbers.

Now we have:

• 32-bit CPUs → Add numbers up to 4 billion

• 64-bit CPUs → Add huge numbers

More bits = more powerful math.

But it’s still all built from tiny switches doing simple things!

⚙️ Where Do the Switches Live?

All these switches (called transistors) live inside the CPU chip.

In fact:

• Your CPU might have billions of these switches

• All packed into a space smaller than your fingernail

So when you click “Add” on your calculator app —
Billions of little switches wake up and do math for you.

💡 Recap: How the CPU Adds and Subtracts

• The CPU adds numbers using special circuits called adders

• It uses binary (0s and 1s) to count

• It handles subtraction by a cool trick called two’s complement

• Everything is built from simple switches

• The ALU is the part of the CPU that does this work.