All language subtitles for 2. Binary Math

So think about it like this when you need to send a signal to a computer and you need to indicate one

you apply current when you want indicators zero.

You don't apply current.

Here we have a cable.

It's turned off no current is flowing binary value is zero.

I'll turn that on.

So current is now flowing binary value is one.

We have two states either current or no current two binary values zero or one.

So one cable two states either current or no current.

If we extend that now and we've got two cables binary value is currently zero zero there's no current

on either cable.

If I put current on the one binary value is now 0 1 change that current on the left no current on the

right binary value is now 1 0 turn them both on.

We've got current on two cables binary value is now 1 1.

So we either have no current on both binary value 0 0 or 0 1 or 1 0.

And lastly 1 1.

We have two states either on or off.

We have two cables two to the power of two is four.

At the moment current is applied the bulb is on that indicates one I can turn that off.

That indicates zero.

So if I want to send you some numbers I could say 1 0 1 0.

And then finally a 1.

Let's put the lamp back on again.

That's how a computer can send information to another computer or that's how programs are written.

We might write a program in a high level programming language like Python but as it goes down we end

up doing assembly language.

We end up writing zeros and ones to tell the computer what it needs to do.

Now the important lesson here is we have two states either on or off.

If we have one cable we have two states on off on one cable.

But if we've got two cables we end up having four states we've either got a 0 0 no current or both cables

or 0 1 0 1 0 or 1 1 current on both cables.

So two states two cables means that we end up having four values.

You can write that as two times two equals four or two to the power of two equals four.

Two states two cables equals four.

Now don't want to spend too much time on this analogy but let's assume we've got three cables in this

example we have three cables.

We've got two states current state is off.

So the binary value is 0 0 0.

Once again and I won't go through all the combinations we could have 0 0 1 or as an example 1 0 1 or

1 1 1.

So we have two states either on or off.

We have three cables.

So two times two times two is eight or two to the power three is eight.

There are eight different combinations or options here.

Now I won't bore you extending that too much but we could do something very similar.

You tell me what binary value do we have here.

If we've got four cables answer is 0 1 1 1.

How many combinations do we have.

We have two states four cables.

Two times two times two times two equals 16 or two to the power of four equals 16 16 different combinations.

In this example they are all on.

We have two states four cables 16 combinations.

So we've either got no current on the first cable no current on the second none on the third none on

the fourth was as an example no current no current no current current or no current no current current

no current.

And if we go through all the possible combinations we're going to end up having 16 binary values.

So two states are shown over here four cables means two to the Power of Four.

Sixteen possible combinations.

Again two states four cables gives us 16.

If we've got two states and we've got five cables that would give us 32 or if we have two states and

six cables that gives us 64 combinations you could manually work this out you could manually go through

every combination.

But we're not going to do that.

But if you wanted to test this and verify that I'm talking the truth then you could do that.

So just to summarize if we've got two states and one cable two to the power of one is two.

So two possible combinations if we've got two states and two cables that gives us four combinations

or four possible states two to the three is eight two to the four is 16.

Now this is one that causes confusion in decimal.

We don't start at one we've started zero and then we count zero one two three ignoring negative numbers

obviously but let's assume positive integer numbers we started zero and then we count up now in binary

we've got two to the power of zero so to two no cables as an analogy equals one.

So we don't start with one cable.

We start with zero cables.

Now this is once again just an analogy.

So if the analogy doesn't work too well for you then just stick with the math.

Just work with a math or maths if you prefer.

So what I need you to remember is two to the power of zero is one two to the Power of One is to two

to the power of two is for two to part three is eight two to the power of 416.

And if we continue to to the power of five is that to two to the power of six or 64 two to the power

of seven is 128 two to the power of eight is 256 but in an IP version 4 address we've got what's called

an octet which is eight binary values.

So we've got eight values but we start counting at zero.

So we've got zero one two three four five six seven let's formalize that by showing you a really important

table.

Now if you're ever going to learn a table then this is the table that I suggest that you learn.

It's really important for the CCMA exam.

Make sure that you know this table before you go and take your exam notice we have at the top here two

to the power of zero two to the power of one two to the power of to two to the power of three four five

six and seven.

Notice we counting from zero to seven but that's one two three four five six seven eight.

If we set this value to one in binary in decimal that equates to one.

If we set this value to 1 in binary it equates to 2.

This value equates to 4.

This equates to 8 to 16 thus to 32 thus to 64 thus to 128.

Remember that two to the power of seven is 128.

And there's our seven 2 to the power of 6 equals 64.

Or if you like two to the power of two equals four.

So when this butt is set on it means fall in decimal.

Now in the real world you're going to use a calculator but you need to understand the basics before

you use calculators.

So we're going to do a lot of this manually first.

And when you take your seat in a exam you can take a calculator into the exam with you.

So you need to know how to do this in your head.

So we're going to do it manually but again for the real world you'll use a calculator so in this table

we have what's called the base exponent.

So we've got starting on the right inside side to triple zero to the power of 1 2 to the power of 2

2 to the power of 3 4 5 6 and 7.

And then we've got a binary equivalent.

So if we set this to binary 1 and then the decimal equivalent is 128.

If I set this to binary one decimal equivalent is to.

To help you understand that let's do an example let's say I gave you a number of Turner 55 255.

If we take the decimal equivalence is equal to 128.

In other words this but is set on 64.

In other words this part is set on 32 16 8 4 2 and 1.

In other words if I add 128 plus 64 plus 32 plus 16 plus eight plus four plus two plus one I get turned

on 55 in decimal that is represented as this in binary so in binary eight binary ones equates to 255

because this equals binary one this equals 128 in decimal.