Hi. I'm Peter Edwards from Bluetutors. We teach children of all ages, right from primary school to degree level, and we find the highest quality tutors, and today, I am going to teach you some math. We are now going to look at how to convert a binary number to a hexadecimal number. So up here, I have written two binary numbers and we are going to look at how to convert both of those. The important thing to note about a binary number and a hexadecimal number is that they are actually related in quite an interesting way. So, the first four digits of a binary number will decide the first digit of a hexadecimal number. The reason for that is that with four digits of a binary number, you can represent in decimal, the numbers one through fifteen, and similarly with a hexadecimal number, the first digit can represent, in decimal, all the numbers from one to fifteen. So, let's look at this first number and let's work out what it is in hexadecimal. So it is a binary number, this column is two to the zero, two to the one, two squared, and two cubed. What I mean by that is that this one means that we have, essentially, two to the power of zero, which is one. This zero means we have no twos whatsoever. This one means we have one four and this one means we have one eight. So, if we convert that into decimal, we have eight plus four, plus zero, plus one, which is thirteen, and in hexadecimal, this is represented by D. Because, once we get to nine, we then have ten is A, eleven is B, twelve is C and thirteen is D. Okay, so that is a simple example to start with. We are now going to move on to a slightly more complicated example. So, again remember each of the four digits represents a number in the hexadecimal system and we have this one on its own. So, let's look at the first four digits of this decimal number. We have one, which represents eight, and another one, which represents four, and then two zeros, which is equal to twelve, and in hexadecimal, that's represented by C. Let's look at the next one. We have no eights, we have one four, no twos and a one, which is five, and also this last one, we just have one. So, we have one, five, and C. So, in hexadecimal, this number is represented by one five C. And that is how to convert a binary number to a hexadecimal number. .

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