Lesson video

Hello, my name is Mrs. Holborow, and welcome to Computing.

I'm so pleased that you can join me for today's lesson.

We are going to be exploring binary numbers in today's lesson, and in particular we are going to learn how to count in binary and how to add together binary numbers.

Welcome to today's lesson from the unit, Representation of Numbers.

This lesson is called Binary Addition.

And by the end of today's lesson, you'll be able to count and perform addition in binary.

Shall we make a start? We will be exploring these keywords during today's lesson.

Addition, addition.

A mathematical operation where two or more numbers are combined to find their total.

Carry, carry.

The extra value that moves to the next column when the sum of digits in a place value column exceeds the base.

There are three parts to today's lesson.

We'll start by counting in binary.

We'll then look at how we perform addition in binary on two binary numbers.

And then we'll finish by performing addition on three binary numbers.

Let's make a start by counting in binary.

Before you can perform addition in binary, you need to learn how to count in binary.

Let's take a look at how we count in decimal first.

The digits that can be put in the 1 place value column start at 0 and go up to 9.

So you can see here, in the place value 1 column, we are counting from 0 to 9.

When 9 is reached, there are no more digits available, and so the next place value column, which in this case is 10, is used.

This is set to 1, and then the digit in the 1 place value column is reset to 0, so 10.

And then we repeat the process.

Like last time, when 9 is reached again in the 1 place value column, there are no more digits available.

The next place value column, which is column 10, is then set to 2, and the digit in the 1 place value column is reset to 0.

This process is then repeated.

This continues all the way up to 9,999 for four digits in decimal.

Aisha says, "So the largest value "four digits can hold in decimal is 9,999?" Jun says, "Yes, and the smallest value is 0!" Time to check your understanding.

What is the highest value that a five-digit decimal number can have? Pause the video here whilst you have a think.

That's right! The highest value a five-digit decimal number can have is 99,999.

It's a similar process in binary.

So here I have my place value table.

Remember, the place values double each time.

So we have 1, 2, 4, and 8 as the place values.

Laura says, "The digits in the smaller columns "start at 0 and then go up to 1." So Laura is correct.

The place value in place value 1 is now 1.

Alex says, "They then spill over to the larger column, "resetting to the smaller column back to 0." So let's have a look at that.

The 1 has gone to the place value 2 column, and the place value 1 column has been reset to 0.

Repeat the process.

Now, this time we've already moved up to place value 4 because there's only two possible digits in the binary number system, unlike in the decimal system where we had 10 possible digits.

Let's see the process repeat again.

1 in the place value 1 column moves up to place value 2, and the place value 1 is reset to 0 and so on.

So you can see it's a really similar process in binary.

It's just that the place value columns are different.

Time to check your understanding.

What would be the binary representation of 6, the next value in this table? Is it A, 110, B, 101, or C, 011? Pause the video here whilst you have a think.

That's right! The correct answer is A.

110 is equivalent to the decimal value of 6.

Okay, you're doing a fantastic job so far, so well done.

Moving on to our first task of today's lesson, Task A, Part 1.

Complete a table showing the binary values for decimal numbers beginning with 0 and going up to the largest decimal number that can be represented by four binary digits.

And as a hint, you're going to need to add more rows as required.

Pause the video here whilst you complete the activity.

For Part 2, what is the maximum number that can be represented by four binary digits? Pause the video whilst you have a think and complete the question.

How did you get on? You're doing a great job so far, so well done.

For Part 1, you were asked to complete the table to show the highest value that can be represented by four binary digits.

So you can see we've added additional rows to the table.

And if we look at the decimal value 15, then the binary value for that is 1111.

Laura says, "I can see a different pattern "of 0s and 1s vertically in each column." Can you spot that pattern? For Part 2, you are asked to identify the maximum number that can be represented by four binary digits.

The maximum number that can be represented by four binary digits is 15, as we saw on our table because that was the last row.

We are now moving on to the second part of today's lesson where we're going to perform addition in binary on two binary numbers.

A bit like counting in binary, adding binary numbers is similar to adding decimal numbers, but there are some differences that you need to be aware of.

There are only four rules to remember when it comes to binary addition.

Let's have a look at what those are now.

Rule 1 is that is 0 plus 0 is equal to 0.

In decimal, this is exactly the same.

Rule 2 is 0 plus 1 is equal to 1.

Again, this is exactly the same as in decimal, so really easy to remember.

Rule 3.

1 plus 1 in binary is equal to 10.

Now, this is where it differs from decimal because obviously 1 plus 1 in decimal would be 2.

And then our final rule, Rule 4, 1 plus 1 plus 1 is equal to 11.

Again, different with decimal because 1 plus 1 plus 1 in decimal would be 3.

Now, Aisha's got a really good point.

"Why would I need to know Rule 4, "or why would I need to add three 1s together "when I'm only adding two binary numbers?" Can you think why that might be the case? Ah, Alex has got a great answer.

"You might have to deal with a carry." So then you would have to do 1 plus 1 plus 1.

Time to check your understanding.

Which is the missing rule from the following rules for binary addition? Is it A, 1 plus 0 equals 1, B, 1 plus 0 equals 10, or C, 1 plus 1 equals 10.

Pause the video whilst you have a think.

That's right! C, 1 plus 1 equals 10 is the missing binary addition rule.

Okay, let's have a look at some examples together.

So here I've got Example 1, and I'm adding together the two binary numbers, 100 and 10.

So I've put them in place value column order like I would if I was doing a decimal addition.

So my first calculation is 0 plus 0, which we know the binary rule for that is that it will return 0.

So 0 plus 0 is 0.

The next column is 0 plus 1, which is equal to 1.

And then the last column, I've got 1, but I've got nothing underneath it.

So that's going to be treated as if there was a 0 there.

So it's just 1.

So 100 plus 10 is 110 in binary.

It's quite useful sometimes to look at the decimal equivalents to check that you've done the calculation correctly.

So 100 is 4 in decimal, 10 is 2, and 110 is 6.

So 4 plus 2 is 6.

We know that that's correct.

So we've done the correct calculation.

Just a reminder.

The empty space in the second binary number is treated as a 0.

Let's have a look at another example, Example 2.

This time I'm adding together the binary numbers 100 and 101.

So first column, 0 plus 1 is 1.

Next column, 0 plus 0 is 0.

And then the last column is 1 plus 1.

Now, what is the rule for 1 plus 1? Maybe pause the video and have a quick think.

That's right.

The rule for 1 plus 1 is 10.

So what we have to do is, because this is the last number in our calculation, is we just put the 10 along the row.

So the answer is 100 plus 101 in binary is equal to 1001.

And, again, we can convert those to decimal, which is 4 plus 5, which is equal to 9 to check our calculation was correct.

Now let's look at an example which shows us how to deal with carried values.

So I've got two binary numbers here, 111 plus 11.

So we know that the rule for 1 plus 1 is 10.

Now, because this isn't the last value in the calculation, we need to use a carry.

So I put the 1 in my carry column and I put the 0 underneath in that first column.

So 10.

Now, we've got the situation here where we have to add 1 plus 1 plus 1, which we know the rule there is, the answer will be 11.

So, again, can cross out the previous carry, and we can carry the next 1 into the next column, which then means we have 1 plus 1, which we know is 10.

So we cross out that 1, and we place it in the column next to the original 0.

So our answer for 111 plus 11 is 1010.

Again, we can do our conversion to decimal to check that we've done the calculation correctly.

So 7 plus 3 is equal to 10 in decimal.

Let's have a look at another example with carried values.

If you want to, you could pause the video here and have a go yourself and then play the video to check that you've done the solution correctly.

First column, 1 plus 1 is going to be 10 with our 1 carried.

Next column, 0 plus 1 plus 1 is going to be 10 again, so cross out that previous carry.

And then 1 plus 1 is going to be 10.

So 101 plus 11 is 1000 in binary.

The equivalent in decimal is 5 plus 3, which is equal to 8.

Okay, it's now time for you to have a go at some calculations.

So on the screen I've got eight different binary additions that I'd like you to complete, and remember to show your workings.

So if you need to carry, remember to put that down and show your workings for that carry.

Pause the video here whilst you complete the activity.

How did you get on? Did you remember the four rules for binary addition? Great work.

Let's have a look at the answers together.

So first one on the top row was 101 plus 11.

The answer for this is 1000.

Next one on the top row was 110 plus 101.

This one's nice and straightforward, there's no carries.

So we've got 1011.

Third one is 1100 plus 11.

Again, no carries for this one.

The answer is 1111.

Last one on the top row is 10011 plus 1001.

And the answer for this is 11100.

Bottom row from left to right.

11001 plus 1110 is equal to 100111 in binary.

Then 10101 plus 1001 is equal to 11110 in binary.

Next one.

11111 plus 10 is 100001.

Lots of carries in that example.

And then the last one is 11101 plus 10110, which gives you the answer 110011.

Remember, if you've made any mistakes or you need to make any corrections, you can pause your video now and do that.

You're doing a great job so far, so well done.

We are now moving on to the third and final part of today's lesson where we're going to perform addition on three binary numbers.

When adding three binary numbers, we follow the same process as when we were adding two binary numbers, and we use those same four rules.

So 0 plus 0 is 0, 0 plus 1 is 1, 1 plus 1 is 10, and 1 plus 1 plus 1 is 11.

In addition, we may need a fifth rule for special circumstances where you have to add three 1s and then also add a carry.

So that's going to be 1 plus 1 plus 1 plus 1, which is 100.

Time to check your understanding.

In binary, what is the result of 1 plus 1 plus 1? Is it A, 10, B 11, or C, 111? Pause the video whilst you have a think.

That's right, it's B.

1 plus 1 plus 1 is 11 in binary.

In binary, what's the result of 1 plus 1 plus 1 plus 1? Is it A, 100, B 11, or C, 111? Pause the video whilst you have a think.

That's right! 1 plus 1 plus 1 is 100 in binary.

Well done.

Okay, let's work through some examples again together.

So I've left the binary rules on the screen so that you can use those.

So this time I've got three binary numbers to add together.

I've got 100 plus 100 plus 10.

First column, 0 plus 0 plus 0 is 0.

Next column, 0 plus 0 plus 1 is 1.

And then 1 plus 1 we know is 10.

Nice and straightforward, that one.

So, again, like we did when we were adding together two binary numbers, we can convert to decimal to check that we've got the correct answer.

So 4 plus 4 plus 2 is 10 in decimal, and we've got the binary result 1010, which is equivalent to 10.

Next example.

1100 plus 10000 plus 110.

First column, 0 plus 0 plus 0 is 0.

Next column, 0 plus 0 plus 1 is 1.

Next column, 1 plus 0 plus 1 is 10.

So we're going to put that 1 down in the carry column.

And then we've got 1 plus 0 plus 1, which, again, means we're gonna put the 1 down in the carry and strike through the old carry.

So 10.

And then the last column, we've got 1 plus 1, which is 10 again.

So the result is 100010.

Which, if we check it back to decimal is 12 plus 16 plus 6, which is 34.

It's now time for you to have a go at completing the following binary additions on three binary values.

Remember to show your workings and your carries.

Pause the video here whilst you complete the activity.

How did you get on? Did you manage to correctly do all of the binary additions? Great work.

Let's have a look at these answers together.

So the first one on the top row on the left was 100 plus 10 plus 1.

Correct answer for that should be 111 with no carries.

So nice and straightforward.

The next one was 1010 plus 110 plus 10.

So the answer is 10010.

Next one is 11100 plus 1001 plus 101.

So the answer is 101010.

And then the last one on the top row.

11100 plus 1010 plus 110 should give you the result of 101100.

Moving on to the bottom row.

11100 plus 10 plus 1 is 11111.

Next one.

10110 plus 10100 plus 10 gives you the result of 1000100.

And then 11000 plus 10010 plus 1001 is 110011.

And then the final one with lots of carries here is 101111 plus 10011 plus 1010.

And the answer for this is 1001100.

Remember, if you need to make any corrections, pause your video here and go back through your workings.

We've now come to the end of today's lesson, and you've done a fantastic job.

You've learned to count and perform addition in a totally new number system.

Amazing work.

Let's summarise what we've learned during today's lesson.

Counting in binary is similar to decimal, but each place value represents a power of 2 rather than a power of 10.

As you count in binary, you move to the next place when you run out of digits, just like moving to the next place in decimal when you go past 9.

Adding in binary works like adding in decimal, but, instead of carrying over at 10, you carry over at 2.

Keep adding each column following the key rules, starting from the right, and handle any carried 1s like you would in decimal.

I hope you've enjoyed today's lesson, and I hope to see you again soon.

Bye!.