Intro Quiz: Number bases

Video: Number bases

﻿Hi, I'm Rebecca your computing teacher for the data representations unit. For this lesson, you're going to need a pen and paper to answer any of the questions that I give you. You're also going to need to try your very best to remove any distractions out of the way so that you can really concentrate in this lesson. Once you've done all of that, we can begin. In this lesson, you will define the term "bit". You'll explain the difference between base two and base 10 number systems, and you'll convert between binary and decimal numbers. Let's think about computers and electricity. Computers use electric circuits and switches to represent all data and instructions. What are the tiny switches inside a computer called? Can you remember from lesson one? They're called transistors. And these are tiny at around seven nanometers. That is super small, if you didn't know. How many do you think would fit across a human hair? Don't worry, you don't have to get the exact answer. So, it's actually 14,285 transistors that can fit across a single human hair. That is an awful lot of transistors there. These transistors allow electricity to be on or off in a circuit. We combine lots of circuits to represent data. Everything in a computer is a represented with a combination of zeros and ones. These switches could represent one zero one zero one one one zero in binary. Let's think about numbers then in the number systems. What is the value of this number, can you say it out loud? It's 9,019. Why does the first nine hold more value than the last nine? It's because each number has a place value. What are the place values in this number? Can you remember what goes at the top? What goes above them? Let's take a look. So, you've got ones, tens, hundreds, and thousands. You work out the next place value by multiplying by 10 as you move from right to left. So there we've got each time it goes up, that number is multiplied by 10 to get the next place value. How many digits are there in our decimal number system then? See if you can count them? How many have we got? So we have 10 digits. Our number system is a base 10 number system because it has 10 digits. Binary is a base two number system. This is because it uses only two digits, zero and one. Make a prediction there. What do you think the place value might be of each of the numbers in this table? Think about what it was for decimal, and see if you can apply that to binary. Let's take a look. So, two, four, and eight, that's supposed to place values. So actually what's happened there is you can work out the next place value by multiplying by two as you move from right to left, just like we did with decimal. Each binary digit is called a bit. To work out the value of a number, you need to know it's place value. You then multiply the digit by its place value. So just take a look at this one. So, if you look there you've got the number nine, and you times that by one because it's in the ones column. And then the one you times by 10, because it's in the tens column, the zero we ignore because it's a zero. And then the nine is times by a thousand, because it's in the thousands column. You then have the answers and then you add them all together, and that makes the final number 9,019. So it's not just numbers in isolation, a nine, a one and a zero. It's a whole number together, nine, 9,019. You do exactly the same thing in binary. If you want to see what it is in decimal. So you multiply the digit by its value, like place value, like what we've got there. And if you look, you've only got ones and zeros there to multiply it by. So just, one times one, two times zero, which is nothing, four times zero, which is nothing, eight times one, which is just eight, isn't it? So, then you add all the values together and you get nine. So that binary value there, one zero zero one is actually nine in our decimal number system. In binary, it's a little easier because you are always multiplying by either one or zero. There's no tens or hundreds of thousands to multiply it in this stage. You don't actually really need to multiply because you either multiply it by the place value or you don't because it's a zero, and it's just nothing. How can you tell the number base of a number that you are presented with? This is an interesting one, I wonder if you'll know. You can actually use a subscript at the end of the number to state the number base. So if you look there, you've got 101 and it's got a base of two, which means that it's a binary number, and you've got 101 with a base of 10, and that means it's decimal number. So, as you see numbers like that throughout this unit, you'll be able to tell whether it's a base two or a base 10 number, by looking at that little number that's been subscript underneath. So, quick recap. Binary, is it base 10 or base two? It's base two, isn't it? And how many digits does decimal have? It has 10, doesn't it? Right, in order to convert from binary to decimal, you need to know the place value of each digit in the number. When you are just starting to learn how to do this, a really good idea tools always use a table like this one, and you'll get quite used to drawing these as we move throughout this unit. So draw this table now, pause the video while you do that. If I give you the binary number one, one, one, then you place the digits from right to left in the table. So just like that, one, one, one. Then you look at their place value and add those values together. So you've got there four, two, and one. You add them all together and you're going to get six. So one, one, one in binary is six in decimal. Let's try another. So convert one Oh one Oh from binary to decimal. And I've already placed it there on the table. So if you can think about it, let's some let's have a go. So you only need to add the eight and the two this time, because those zeros don't need to be included. So you just do eight add two, and that equals 10. So one Oh one Oh in binary is 10 in decimal. Let's try a slightly larger number, then. Convert one, zero, one, one, one, one, from binary to decimals. So you can pause the video and see if you want to have a go at it, or you can just follow along in a few seconds. It's up to you. But what you've got to do, first of all, you got to see which ones have got ones underneath them. And it's all of those. And then you've got to add them all together. So one, zero, one, one, one, one in binary is 47 in decimal because it's the total of all those ones with a one underneath them. Use your table to how you answer the following quick fire questions. Now I'll try not to be too fast when it gets a little bit harder, but you can always pause the video, if you need to, if I am going too fast. So don't panic. If I'm going too fast, just pause me. 'Cause that's what it's there for, okay? Let's have a go. So convert these numbers from binary to decimal. See if you can do it. So 101, what that in decimal? It's five. One, one, one, one, what's that in decimal? It's 15, okay? So one, zero, one, one, one, it's getting a little bit trickier now. it's 23. One, one, one, zero, which one is it? It's 14. And oh gosh, that is a super big one. What's this going to be? It's 131. Wow, that was, quite intense, wasn't it? It's a little trickier to convert from decimal to binary. You need to work from left to right this time and you need to subtract, not add. So it takes a few extra thoughts as you do this. So let's start with a small number, which is number five. So if I wanted to take the decimal number five and convert that to binary, then this is what I needed, this is what I would need to do. So you start by looking for the highest value that fits into that number. So you can go down the list. 16 doesn't fit into five, nope. Does eight fit into five? Nope, does four fit into five? Yes it does. So once you found one, you put a one, and then you've got to start doing your subtraction. So you take the original five, and then you take away four, 'cause that's the place value that you've just used and you're left with the value one. Then you start looking for the highest value that fits your remaining number. So does two fit into one? Nope. Does one fit into one? Yes, it does. And you're left with that. So five, in decimal, is one 101 in binary. You can double check your maths by doing a quick conversion back to binary, to just make sure. So one in binary, 101 in binary is five in decimals. So you just have a look at those bits on the top. So, four add one, that's five, yes we're right. And this becomes more essential with numbers, especially if you're in an exam, because it's so easy when you're under stressful conditions, like an exam, to make tiny little errors with numbers, so it's always a good idea to just double check your working out. And I just do this out of habit. I always check it every single time. I don't trust that I'll get it right the first time. I always go back and check, and it's really good to build that habit quite early on. And also it gets your brain working as well, 'cause it means you get to practise converting it the other way too. 'Cause you don't want to miss out on a mark in the exam just because you counted a four instead of a three or something like that. So it's very important that you always double check. Let's try a higher number, then. Convert the decimal 60 into binary. So do exactly the same thing. What is the highest number in our table that will fit in to 60? So it's 32, isn't it? 'Cause 64 doesn't fit into 60, does it? So you do 60 takeaway 32, which is 28. So that's what you're left with. And then you go down the list. So does 16 fit into 28? Yes it does, so I put a one there. And then you left with 12. And then you start looking again. So, what is the highest value that fits into 12? It's an eight. So we put a one there. 12 takeaway eight equals, four, so now we're left with four. What is the highest value that fits into four? Well, the next one along is a four. So you've got to put a one in that one too. And you do four take away four, which is zero. So you don't need to make any more numbers. So you just put zeros in those remaining columns because you've got to the end of that number. So we have our answer. 60 in decimal is one, one, one, one, zero, zero in binary. So, we can double check, always important to double check. So count up all of those ones. So 32 add 16 add eight add 45, and if you add all of those up then you're going to be left with 60, so we got it right. So try these conversions from decimal to binary by yourself. Now, see if you can do it using the table. Pause the video while you do that. Let's go through those answers then. So the first one, 128 is one zero zero zero zero zero zero zero. So I think it's absolutely right amount of zeros. Of course it's just a one and then later zeros, because you've already 128 fits into 128. So you just put a one there and the rest are going to be zeros 'cause you've got no numbers left. 120 was one, one, one, one zero, zero, zero. 80 was one, zero, one, zero, zero, zero, zero. 200 was one, one, zero, zero, one, zero, zero, zero. 190 was one, zero, one, one, one, one, one, zero, okay? Hopefully you got some of those right, or most of them right, let's see. Do your thumb. How well did you do, did you get five out of five? Well, three, four, five is going to be good, isn't it? It's because we're just practising our way. So you might get a few wrong. But hopefully you remember to double check them and take them backwards as well to make sure that they were right. So that is all to do then with give, getting you started with binary. And hopefully you've got an understanding of how binary works and how we can actually convert those numbers from binary to decimal and decimal back to binary. If you'd like to, please ask your parent or carer to share your work on Instagram, Facebook, or Twitter. So you could tell me how many you got out of five on that last one, tagging at @OakNational and #LearnWithOak 'cause we'd really love to see what you've been up to. And I'll see you soon for lesson three.

Exit Quiz: Number bases

Completed: Number bases

In this lesson, you will use decimal representation to explore the concept of place values in number bases and the values of digits. Then, you will explore the representation of binary values, and converting these back to decimal.

Computing

Number bases

Introductory Quiz

Video

Final Quiz

Lesson Complete