I wish I could see how computers really work.
Computers see everything as ones and zeroes.
Even me?
AAARGH!
What’s happening!?
Where AM I?
You’re inside your computer!
You SAID you wanted to see how they work.
Couldn’t you just tell me?
Now what?
To get around in the computer world, you’re going to need to speak binary.
What’s BINARY?
Binary is a system of numbers that has only two digits, 1 and 0.
No twos?
Or threes?
Or fours?
Or fives?
Or…
Nope, just two kinds of numbers, one and zero.
Why would you get rid of all the other numbers?
The binary system is very useful in electronics, because you can use the ones and zeroes to
stand for on and off.
Like flipping a switch?
Exactly.
Imagine zero stands for OFF, and one means you’ve switched it ON.
Okaaay...
I know it can be confusing, because you come from a decimal world.
Decimals?
We have 10 fingers.
So we get used to counting by 10s.
That’s what decimal means.
Deci- means 10.
Like how decade means 10 years?
Right.
So when you count up on your fingers, you’re counting digits.
Each finger stands for one.
I know how to count to 10 using my fingers.
Let’s count together.
But start with zero - no fingers...
0 1 2 3 4 5 6 7 8 9 10.
Good.
What happened when you got to the last digit?
I said TEN.
Right.
But notice that you used two numbers to stand for that - a one and a zero.
You put a one in the TENS place, and a zero in the ONES place.
Oh, yeah, I guess I did.
The same thing happens when you get to 99 and then a hundred.
You put a one in the HUNDREDS place, a zero in the TENS place, and a zero in the ONES
place.
Well that only seems natural.
You’ll see, Topher, that we do something really similar in the binary system.
Okay, I trust you.
Sounds weird, though.
{Computer voice reads binary numbers}
Now let’s try counting in the Binary system.
Remember, you can only use ones and zeroes, no other numbers.
I’m really not sure how to do this...but I’ll try.
First, no switch is lit up.
ZERO!
Good.
Now, light up one switch.
ONE!
Now let’s light up two switches.
2...I mean...no.
Wait.
I don’t know.
I can’t use a two!
That’s right.
So we move to the next PLACE.
And we put a one there.
Just like going from 9 to 10 in the decimal system.
So...I think it would be...One...zero.
That stands for two?
Yes!
Good, Topher!
Let’s light up another switch.
One...one.
That stands for three!
Yes.
Now another switch.
Move that one...so now it's
One zero zero.
That’s four!
Good.
Turn on another switch.
One zero one.
That’s five!
What would be six?
One one zero.
Seven?
One one one!
I like that one.
Me too.
How about eight?
Have to move that one to the next place, so...one zero zero zero.
Good.
Nine?
One zero zero one
Yes.
Ten?
One zero one zero.
Perfect!
You did it, Topher!
You counted to ten in binary!
But Ulka, what is all this counting in binary for?
This is how you store information in a computer.
The state of every switch, whether it’s on or off, is stored as a binary digit, 0
or 1.
We call binary digits “Bits” for short.
We put the two words together.
BI - nary dig - IT.
Hahaha I get it.
BIT.
BI -nary dig -IT.
And we usually store them in groups of 8, called bytes.
8 bits to a byte, okay.
But Ulka, is there a faster way to do this than just counting up switches one by one?
I’m glad you asked, Topher.
The whole point of using binary is that it’s very fast.
So let’s learn the fast way of converting between decimal numbers and binary numbers.
YAYYYY!!!
Calm down Topher.
You need to concentrate to understand this.
Okay, I’m concentrating.
This is my concentrating face.
First, it helps to know the powers of two.
How powerful can two be?
It’s just a little number.
No, Topher, the POWERS of two.
Have you seen numbers with exponents?
Like this: 2 to the zero power is 1
2 to the first power is 2 2 to the second power is the same as 2 times
2, which equals 4.
2 to the third power is the same as 2 times 2 times 2, which equals 8
Topher: So 2 to the fourth power is 2 times 2 times 2 times 2, which equals 16!
Very good, Topher.
What’s 2 to the 5th power?
2 x 2 x 2 x 2 x 2 = 32.
2 to the 6th?
2 x2x2x2x2x2 = 64
Okay, I think you have the idea.
So let’s start converting.
First, let’s convert from binary numbers to decimal.
To do this, we add up all the places.
Each place that has a one in it stands for a power of two.
Remember the first place is the ZEROES place.
Here’s our first example.
The binary number ONE ZERO ONE.
In decimal, that equals 2 to the ZERO, which equals one, plus…
Nothing for the 2 to the one place, plus 2 to the second equals four.
Add it all together: 1 plus 4 equals 5.
Huh.
Next example.
ONE ONE ONE.
To make it a decimal number, add up 2 to the Zero equals one, plus
2 to the one equals 2, plus 2 to the 2 equals four.
You get 1 plus 2 plus 4 = 7.
Oh, yeah, I remember that one.
Let’s do one more example.
This one’s bigger.
ONE ZERO ONE ZERO ONE.
In decimal, that equals 2 to the zero equals 1, plus
Nothing for the 2 to the 1 place, plus 2 to the 2 equals 4, plus
Nothing for the 2 to the 3 place, plus 2 to the 4 equals 16.
Add all that up together: 1 + 4 + 16 = 21.
Okay, Ulka, I understand!
But what about going in the other direction?
What if I know a number in decimal, but I want to figure out what that is in Binary?
That’s a little harder.
But we can do it!
Ready?
Ready.
Ooh, can we convert my favourite number, 42?
Why is that your favourite number?
I don’t know, I just like how it sounds.
Okay Topher.
The first step is, you subtract the largest power of 2 that is less than or equal to 42.
Well, 2^5 is 32, and 2^6 is 64.
32 is the largest power of 2 less than or equal to 42.
So that means we subtract 32.
Good!
Put a one in that place of the binary number.
So put a one in the 2 to the fifth place.
Okay.
Next, you subtract the next biggest power of two possible from the remainder.
42 minus 32 is 10.
2^3 is 8, and 2^4 is 16.
8 is the largest power of 2 less than or equal to 10.
So we subtract 8...and get 2 leftover.
Right.
And put a one in the 2 to the 3rd place.
We have 2 leftover, which is 2^1.
Good!
So we put a one in the 2^1 place.
Let’s fill in all the other places with zeros.
So we get…
ONE ZERO ONE ZERO ONE ZERO
That was harder, Ulka.
But we did it!!
Um...Ulka, are you ready to go home now?
I think we should do a little more practice first.
Ooooohh
{Topher and Computer Voice read binary numbers}
Are you proud of yourself?
You learned something today!
I feel great, Ulka!
I speak binary now!
Ready to go home?
01111001 01100101 01110011
We may have overdone it.
Now it’s time to watch more videos from Socratica Kids!
Pick this one...or this one…
or 010111101010101....
Whoahhh I'm turning into a computer!