I built a 4bit Adder

What is a 4bit Adder? Well, a 4bit adder is a circuit used to add numbers up to 15, meaning we can do 225 different calculations with this circuit. Here is a picture of the wiring of a 4bit Adder.

So basically, this is a very small part of a processor. Processors are dedicated to doing math around your computer, so having tiny calculators like this are the fundamental pieces of automated math computations. So you might be wondering, “What is this full adder nonsense?”. Well, before I can explain what a full adder is, I have to explain what a half adder is. So a half adder is basically a circuit that can add binary numbers like this.

0+1 = 1

1+0 = 0

And of course,

1+1=2

now wait a second…

There is no 2 in binary, so it would actually be:

1+1=0 carry 1

This circuit is created usingan AND, an and XOR gate.

An AND gate detects if both A and B are the same, example:

IF A=TRUE AND B=TRUE:

THEN RETURN TRUE

IF A=TRUE AND B=FALSE:

THEN RETURN FALSE

XOR is completely differentthan OR,

XOR is true if A and B are different, example:

IF A=TRUE AND B=FALSE:

THEN RETURN TRUE

IF A=FALSE AND B=FALSE:

THEN RETURN FALSE

Perfect we finally figured it out, all good right?

Well not exactly, what if we had a problem like this?

(carry 1 in) 1+1=?

Well, we can’t compute this with a half adder as it has no option for a carry in.

So (you might be thinking), how are we going to go about doing this?

Well here she is, quite a beaut. This is what is called a Full Adder. A Full Adder can do computations better than a Half Adder, as it can use carry ins.

With carry ins, it might look like we have strapped a half adder with some Velcro to the other. And you would be partially right except for one thing. As you can see in the bottom right there is an arrow with, “>1”,on it.  This is an OR gate and this is what allows for there to be a carry in.

With this new circuit we should be able to do a computation like this.

(carry1 in) 1+1=1carry 1

Beautiful, but a little bit limited, we don’t just want to add one number to another, we want to add larger numbers like 265454+876543234+245676543. Well, hopefully not that big but at least a number like 13 + 4. To go about this we must (once again) strap a bunch of full adders together, as shown below.

Here we go, now we can add four digit binary numbers.

For example here is a problem I made to test it.

1011

0110

=

10001

1011(binary for 11) + 0110 (binary for 6) = 10001(binary for 17) 

And there you go, a super cool binary calculator that can add up to 15+15. You can now assume that if you strap more of them together you could have an even better calculator

Anyways, that’s all I have. Hope you like getting forced to learn computer engineering, I thought it was pretty great but that’s just me.

-Lordwhitebear 2017