How To Convert Decimal To Hexadecimal

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. Today, I'm going to teach you some maths.

We're now going to look at how to convert a decimal number into a hexadecimal number. The first thing to do is briefly go over what a hexadecimal number's digits mean. So we're only going to look at three digit hexadecimal numbers at the moment.

So the first digit represents units sixteen to the power of zero which is one, which is units. The second digit represents sixteens and the third digit represents sixteen to the power of two which is two hundred and fifty-six. So an important thing to do when you're working out how to convert a decimal number into a hexadecimal number is to start off by working out how many digits that hexadecimal number is going to have.

The first example we're going to use is seventy four. The first thing were going to do is decide what we're going to do in terms of how many digits this hexadecimal number is going to have. Since two hundred and fifty-six is less than seventy-four, we know there are only going to be two digits.

So we now want to see what we're going to put in this first column for the sixteen to the power of one. To do that, we divide seventy-four by sixteen and the result of that is four. Four times sixteen is sixty-four and so the remainder that we have from that is ten.

Now, ten is obviously a single digit in a hexadecimal, simply represented by A. Therefore, this tells us that seventy-four when written as a hexadecimal number is four A. Okay, so now we're going to move on to a slightly more complicated example, and we're going to try and represent six hundred and eighty as a hexadecimal number.

Now, you'll notice six hundred and eighty is greater than two hundred and fifty-six, so we're going to have three digits in a hexadecimal number. What we're going to do first is divide two hundred and eighty by, so we're going to divide six hundred and eighty by two hundred and fifty-six. The result of that is two.

Two times two hundred fifty-six is five hundred and twelve. So our remainder is one hundred and sixty-eight. Next, we're going back to what we did in the first example, and we're going to divide one hundred sixty-eight by sixty.

The result of this is ten. Ten times sixteen is one hundred and sixty, so we're left with a remainder of eight. So we're going to put eight here.

Now, we have the three digits in our hexadecimal number, you'll notice again that we have ten which is represented by A, so this tells us that six hundred and eighty when written as a hexadecimal number is two A eight. That is how to convert a decimal number into a hexadecimal number. .