How To Convert Hexadecimal To Decimal

Hi. I'm Peter Edwards from Blue Tutors. We teach children of all ages, right from primary school to degree level.

We find the highest quality tutors. And today, I'm going to teach you maths. We're now going to look at how to convert a hexadecimal number into a decimal number.

So before we do this, we need an understanding of what hexadecimal number is. Quite simply, in what we would normally call the tens column when we're now calling the sixteens column and what in we normally call the units column, it's still the units column but it can also contain the letter 'A' to 'F'. So let's look at how to convert 3A into a decimal number.

So we have three in the sixteens column. So we're going to say three times sixteen and we have A in the units column. Now, A represents the number 10 in hexadecimal, so that's adding ten and three times sixteen plus ten is equal to fifty-eight.

So the number 3A in hexadecimal is equal to fifty-eight in the decimal. Let's move on now to a slightly more complicated example, just because it's a slightly bigger number. F represents the number fifteen in hexadecimal.

So this time, we're going to have fifteen times sixteen and again one, one is just one, so we're going to add on one at the end. And this is equal to two hundred and forty plus one which is two hundred and forty-one. So the number F1 in hexadecimal represents the number two hundred and forty-one in decimal.

Okay. So our third example is a bit more complicated still. We still have digits in the units column and the sixteens column but now, we also have a digit in the sixteen square column.

Now, sixteen square is two hundred and fifty-six. So we have four times two hundred and fifty-six. We have A times sixteen, A is represented by, well, A in hexadecimal represents the number ten in decimal.

So that would be adding ten times sixteen, and B in the units column, which represents eleven in hexadecimal, so we're going to add eleven. So now what we have to do is multiply all of these together. So four times two hundred fifty-six is one thousand and twenty-four, ten times sixteen is a hundred and sixteen and also we're adding on eleven.

And when we add all of those together, we get thousand twenty-four plus hundred sixteen is one thousand one hundred and eighty-four plus eleven is one thousand one hundred and ninety-five. Therefore, 4AB is hexadecimal represents one thousand one hundred and ninety-five in decimal. And that's how to convert a hexadecimal number into a decimal number. .