Hi, I'm Peter Edwards from Blue Tutors. We teach children of all ages from primary school right through to degree level and we find the highest quality tutors. And today, I'm going to teach you some maths. We're now going to look at converting a decimal number into a binary number. So, the first thing to do there is to understand what a binary number is. A binary number represents powers of two basically. So the first digit represents two to the power of zero, so that can either be one or zero as can all of the digits. The second digit represents two to the power of one, the third two to the power of two, the fourth two to the power three, and so on. So we have one, two, four, eight, sixteen, thirty two, sixty four, and one hundred and forty eight. And a binary number can represent any decimal number that you choose. So, we're going to look at a few examples, so we're going to try and convert twenty five into a binary number. The first thing we have to do is look at the leading digit of that binary number. So seeing as twenty five is less than thirty two but greater than sixteen we know that the leading digit is going to be in this column here. So we're going to have a five digit binary number. What we're going to do is divide twenty five by sixteen which is one and we get a remainder of 9 and essentially then we just repeat the process. So we look at where nine is, we're going to divide by eight. Nine divided by eight is again one and we have a remainder of one. In this case going down we look at four. Now when we divide one by four we get zero again with a remainder of one. If we go down again, divide by two, zero, remainder one, and lastly, clearly when we divide by one we get the result of one. So we have our number here so this tells us that twenty five in decimal is equal to one one zero zero one in binary. Okay, so now we're going to look at another example which is slightly more complicated. Again we need to decide on how many digits this number is going to have when we convert it into a binary number so a hundred and seven is greater than sixty four but less than one hundred and twenty eight so we're going to start by dividing a hundred and seven by sixty four. The result of that of course is one, and the remainder is forty three. So we're now going to divide by thirty two, the result again is one and the remainder is nine, we divide that by sixteen and we get the result of zero with the remainder of nine. Divided by eight gets the result of one with a remainder of one. Divide that by four, also zero, remainder one. Divide by two, a result of zero, remainder one, and finally dividing by one gives us a result of one. So we can see from this that a hundred and seven in decimal is equal to one zero one zero zero one in binary. And that is how you convert a decimal number into a binary number. .

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