Original subtitles

Hi, guys.

So in this lesson, we're going to learn binary format numbering, whether you want to or not.

Oh all right.

No, no.

This one's a doozy.

So you'll see what I mean in just a moment as we get started.

So very simply, right, the base of the binary number system is to.

And in this system, only numbers zero and one get used.

So each zero or one digit in the binary numbers system is defined by binary digit.

OK, so first, let's try to understand the binary to decimal logic.

In fact, we'll start right away with an example.

So we'll go through the example on the screen and you can see from the tables zero or one at the very

far right of a binary number sequence is multiplied by two to the zero.

A zero to one to the left of it is also multiplied by two to the first power.

OK, so this system continues as a power of two increases as you move out to the left.

So when we look at the example above, we can see that two to the zero equals one.

Two to the one equals two to two, the two equals four.

Due to the three equals eight two to the fourth equals 16 due to the fifth equals 32 to two.

The six equals 64.

Two to the seventh equals one 128.

So since one has written in each digit, we evaluate that the value in each digit is valid and add these

digit values.

And then the result is 255.

OK, so we'll continue with the example below.

So likewise, the rightmost digit will correspond to to to the zeroth, and the exponent of two will

increase as you move to the left.

But here we see there is no one in every step.

Wait, no, no.

For this reason why we include the values in the digit that says one in the addition process.

We're just not going to include the digits, the right to zero.

So starting from the right, we'll need to add up the first third, fifth eight digits C.

So as a result, this result right here in this example, there's some of the numbers due to the zero

equals one to two, the second which goes for two to the fourth.

She was 16 to the seventh equals one eight and that will be 149.

Well, now that makes you an expert in binary to decimal logic.

So now that you got that, I want to focus on decimal to binary logic.

What?

Yes.

Again, let's try to look at the subject through an example.

So you can see on the screen we will try to convert the decimal number 25 into the binary number system.

Go ahead.

No, I'm just kidding.

That conversion process actually has more than one method, but for now, I just want to tell you about

the easiest and most widely used one.

OK.

So when we want to convert any decimal number to a binary number, we start to create a table.

Like you see on the same screen.

And we write the number that we have 25, for this example, at the beginning, and we'll write two

over here on the left side.

Now, the purposes of these TOS is that we're going to continue dividing our number and each result

by two.

So in other words, first will divide 2005 by two.

Now I know the result is actually twelve point five, but in this system, we will only focus on integers

and proceed with the logic of doing a first division that we learned in our lives.

Right.

So when we divide five by two, the result is 12 and the remainder is one.

Mm hmm.

So the results are the remainder here are very important to us.

So therefore, when writing the results at our table, you should note, please the remainder on the

side.

And when we divide our new result 12 by two, the result is six the remainder zero.

So we continue with this logic until the result is zero.

And finally, we write the remaining numbers that we noted on the right side from bottom to top.

And as you can see on the screen, we find it the equivalent of 25 in the binary number system is one

one zero zero one.

Wow.

Good for you.

See, now if you can't actually be sure the result, after finding the binary equivalent of a decimal

number at first, you can always verify it with the binary to decimal logic.

So for this example, let's do it.

So here we've reached 25 from the sum of the numbers to two, the zero equals one to the third equals

eight to the fourth equals 16.

And see, we've realized that our result is correct.

So I think that both conversion processes are fairly easy and even enjoyable.

But of course, that's just me.

It may be difficult at first, but after a little practice, I'm sure you're going to get up to speed

and you're going to have a lot of fun doing these kind of transformations.

All right.

Now that's it for this.

We've learned decimal to binary and binary to decimal conversions.

So that's cool.

Let's see in the next lesson, though not still going to be good.