Hello, my name is Typhoon, and in this lecture you will get detailed information about converting
the decimal to binary and vice versa, as well as converting the hexadecimal to decimal and vice versa.
In the world of computers, data is represented using binary digits, commonly referred as zeros and
ones.
Right?
So a binary is the fundamental language that computers use to perform calculations and store information.
However, as humans, we are more accustomed to working with decimal numbers, in this case decimal
here.
Decimal means base ten.
Actually, let's make, uh.
Let's use a different color for this here.
So.
Base.
And hexadecimal means.
Hexadecimal.
Means we call the decimal base.
Gazette.
Gazette Yes.
Page 16.
So here, therefore, understanding the conversion between these different numbers, for example, turning
the decimal to turning the base ten to base 16 or vice versa, turning the converting the base 16 to
base ten is important in computing.
And here in this lecture we will explore in detail how to convert decimal to binary and vice versa.
And you will also learn how to convert the hexadecimal to decimal like this here.
So and vice versa.
So here we will.
Firstly, we will firstly.
And we also have the binary here.
A binary.
And this here we tell this binary only.
Once and.
Zeros or zeros and ones so false or.
Oh, and here, actually, let's.
At this brush here.
The light.
This.
As we will write things on the screen.
Okay.
And also we can also.
Okay, so now we will first start with converting the decimal to binary.
Now let's delve deeper into the process of converting decimal numbers to binary.
And the key concept here is understanding the significance of each digits position in the binary representation.
So.
And the as I said, the binary system binary number system follows the base two.
So remember base ten, base 16 and base.
You're right.
Now, we will delete this because I think we understood that already.
Delete that.
Or converting the decimal to binary.
And in this case, so as I said so and this base two system where each position here represents a power
of two.
So starting from the high mass position, also known as the least significant bit.
So the positions are here.
Q power of 0 to 1, two of three and so on.
So with the exponent increasing as we move to the left.
So it works like this, right?
The first here.
So it works a reverse in, in reverse order here.
So let's actually draw it again.
So.
And now what we're going to do is we will begin with the decimal number you want to convert to binary.
In this case, let's actually write our the title here.
Uh, decimal.
To.
Binary.
In this case.
Here we will.
Let's select the number we want to convert is the 30.
Six right here.
So the first step here, the first step, let's actually we will also write the step steps here.
So the first step.
The first step is we'll begin with the decimal number you want to convert to binary.
Here in this case, it's 36 here.
So in this case it's 36.
And the step two is we will divide the number by two and note down the remainder.
So we will 36 divided by two and we don't have any remainder.
So in this case, it is the zero.
And the step three is continuing, dividing the quotient by two until the point becomes zero.
Right.
So in this case.
We will.
Also 36 divided by two.
And in this case, we will not have the 36 anymore because we already divided it.
So we will need.
Actually.
Let me get the pen here.
Uh, the.
Purser.
So in this case, we will have the 36 divided by two.
So we have the number reminder is zero, but we also have the.
You need the color?
Yes.
Perfect.
Now we will.
We have the remainder of zero and we have the 36 divided by two is.
18.
So we will note that down 18 and the remainder zero.
And here now, we will divide our 18.
It you again.
And here we also have zero.
So now we will in the we will we will continue dividing the quotient by two until the quotient becomes
zero as well.
Uh, so.
Here.
We will now 18 and we what we have left here is nine.
So step four again.
And nine two again.
And as you can see here, we have one reminder here.
And our.
Here is for.
And now we will again.
Step five is.
Or divide by two.
Zero and two.
And.
Thanks again for divide by two again.
Oops.
Two divided by two by two.
We don't have any reminders.
And we have one here.
And here this is the last step almost for calculating our binaries.
So now we need to divide one by two.
Right.
So step seven, divide one by two.
In this case, we will have zero.
But we left with one reminder.
Right?
So and this is our step.
So let's actually so we actually in this case, in the as a result, we don't need this numbers anymore.
So this is our result which now oops actually.
So our result is starting from top 001001.
And here this the the last step here we will need to write down all the reminders in reverse order and
that will be the binary representation of our decimal number in this case is we will need to.
Right down from the from the.
From the bottom.
So here what we're going to do is so our result is actually let's get the span here again.
Let's color actually let's change the color here.
Okay, so here, this is our result.
So when we turn 36 to binary, we will get this here.
One.
Zero.
And here 100 from the bottom.
So reverse order and again, 100.
So 100.
So this is the decimal representation.
So this is the binary representation of our 36 decimal number awaiting you in the next lecture.