Let's talk about logic! Do you know what logic is? Logic is somekind of mathematics, mixed with philosophy in simple word. It's started by Greek philosopher, Aristotle. Simply, logic says : John is taller than Ali, Ali is taller than Ahmed, so, John is taller than Ahmed. This was a very, very simple example of a logical problem in our daily life. We can do this example for everything measurable in our daily life, souch as area, height, weight, etc.
We have some simple logics, and we review all of them here, and we solve some simple problems, and create new logics.
As we have binary system, we use 0 for everything off and 1 for everything on. 0 for everything true and 1 for everything false. So, here we have just one variable called A. Let's do NOT operation on A!
| NOT | A | ~A |
|---|---|---|
| 0 | 1 | |
| 1 | 0 |
We show NOT A in this form :
~A
This notation, helps us write logical functions. Functions are operations we do on one or more variables, and it has unique answer per inputs from a bunch of variables.
This operation, is very simple, but has two logic inputs. The table of AND is like this :
| AND | A | B | Out |
|---|---|---|---|
| 0 | 0 | 0 | |
| 0 | 1 | 0 | |
| 1 | 0 | 0 | |
| 1 | 1 | 1 |
We show A AND B in our logical notation like this :
AB
Of course, you remember famous question from Shakespear's novel Hamlet, To be, or not to be; this is the question!. Now, we're going to explain what OR is. This table can explain this operation :
| OR | A | B | Out |
|---|---|---|---|
| 0 | 0 | 0 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 1 |
One of operations needs to be True, and it makes whole answer true.
And, we show A OR B like this :
A + B
You saw, we used a table, which includes inputs and outputs, and also operation. This table is called Truth Table.
So, let's combine some logics and make new ones! The simplest ones are :
It means :
~(AB)
It's NOT(AND(A, B)) in a simple word. And we draw truth table like this :
| NAND | A | B | Out |
|---|---|---|---|
| 0 | 0 | 1 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
It means :
~(A+B)
It's NOT(OR(A, B)) in a simple word. The truth table is like this :
| NOR | A | B | Out |
|---|---|---|---|
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 0 | |
| 1 | 1 | 0 |
Is there any more logics? of course yes! But, we will have a view on two others, in this chapter.
There are to other logics, which are made from other logics, I would like to call them "Complex". Because They're not as simple as NAND or NOR. Also, we can call them "Exclusive Logics". This is what other engineers called them.
This logic, is implemented like this :
~AB + A~B
So, we will have a truth table like this :
| XOR | A | B | Out |
|---|---|---|---|
| 0 | 0 | 0 | |
| 0 | 1 | 1 | |
| 1 | 0 | 1 | |
| 1 | 1 | 0 |
This logic is the same as XOR, but with a little difference! If you apply a NOT function to XOR, you'll get XNOR. But, the best implementation of XNOR is this function :
~A~B + AB
And we'll get this truth table :
| XNOR | A | B | Out |
|---|---|---|---|
| 0 | 0 | 1 | |
| 0 | 1 | 0 | |
| 1 | 0 | 0 | |
| 1 | 1 | 1 |
Now, we know logics, and we need to learn about Logical Circuits, which are representation of these logics in computer science and electronics. In next chapter, we will learn how to use and design simple logical circuits, and then, we start designing and implementing our dear micro-controller. Of course you needed these chapters to learn the computer language, but after learning the language, you need to know how a computer is built!