##### How an ALU works.

Hey.

I hope you are well.

Let's start.

# What is an ALU?

The ALU, or arithmetic and logic unit, is a component inside your computer that performs, well, *arithmetic and logic*.

It used to be it's own chip but now is embedded in your CPU.

To understand the ALU is to understand logic gates so we will go in-depth on those as well.

# Logic gates.

Think of binary.

It uses 1s and 0s right?

So two values.

- 1
- 0

Think of something that also uses two values.

Bools!

- True
- False

And we need 1 more thing to complete this logic.

Electricity!

The absence of electricity flowing through a wire is represented as a 0 and an electric current is represented as a 1.

- On
- Off

So we can map it all up like this:

#### The chart:

- Bools
- True
- False

- Binary
- 1
- 0

- Electricty
- On
- Off

Okay!

So now that we have that established how do we make logic gates?

Well, we can connect certain transistors in a way that it creates these circuits.

The main gates we use are the following:

- AND
- OR
- NOT
- XOR

Let's discuss these in detail.

## AND gates

Above is the symbolic representation of an AND gate. We abstract away all the wires, and use this symbol.

The *typical* AND gate takes 2 inputs (A and B) and returns 1 output. This output (if we represented electricity as binary) is A * B.

Note that if we added, for example C, it would be the same output but it would be A * B * C.

## OR gates

The *typical* OR gate takes 2 inputs (A and B) and returns A + B.

But wait, you might be saying, binary has no representation of 2! Well if it has a 2 it just makes it a 1.

Again, note that if we added, for example C, it would be the same output but it would be A + B + C

## NOT gates

The NOT gate takes 1 input and returns the opposite of it.

Example:

- 1 turns into a 0
- 0 turns into a 1

## XOR gates

The XOR gate is very similar to the OR gate.

If **only** one of the inputs is 1 it returns a 1.

Again, note that if we added, for example C, it would be the same output just with 3 inputs and only 1 could be on.

# How is this relevant to the ALU?

The ALU uses these gates to make *circuits*.

For example:

This is a half adder. It takes two inputs (A and B) and combines them. If there is a carry into the next bit though. It will send a 1 on the carry line.

This can be used to make this circuit:

Which is a full adder. It s the same as the half adder but takes 3 inputs.

And we can use that to make this:

It is an 8-bit ripple-carry adder. It can add 8 bit numbers.

# Conclusion

If you enjoyed, upvote.

And the ALU is *very* complex but *very* cool.

great tutorial!

Hi @Wuru, thanks so much for the helpful and concise explanation in plain English - excellent 😀

Thank you, it is kind people like you that keep me motivated to create these tutorials. @rjlevy

@Wuru thanks - I can see you put a lot of effort into it. It was very easy to follow. What other tutorials have you created?

Thanks @Wuru - I'll check them out. You don't often see tutorials on repl.it

No problemo. @rjlevy

Wow!! Awesome!

bootiful

An ALU may be complex, but an allu is a Finnish guy who shoots you in the head.