# Decimal to Binary Conversions

There are two possible ways: a more technical one, which is also used in the Cisco Courses for Networking and presented in most sources, while the other one is less used and more of a scientific method.

I will only show you the Cisco method and if you really want to use or know about the other one you can ask and I will add it to this article or send it to whoever asks for it. This method is the most appropriate and less time consuming while also technical and simple.

This is also the backwards process of the one you saw in the post about the Binary to Decimal Conversion.

We will draw another table of the same format, the only difference being that this time we will have the decimal row first and as for the binary, we will have to find it out. This time there will be no preset help, so we will actually follow each step. The basic concept behind this method being now that we have a given number, for example 202. We will have to check each position with the corresponding decimal value if it is contained inside the actual number, and the rest we get after each reduction. Each time we find a number is contained by the original 202 one, we will remove the value from it continuing the exercise with what is left. For each time the decimal number of the corresponding position fits inside the original number, we will set a 1 for true on the binary row, and a 0 if the value can’t fit. The best way to explain is to follow the example.

The first thing we would do is to compare 202 with 27 which is 128. 128 is contained inside 202 once, and if we do a basic math operation of reduction, like 202-128 we get a rest of 74. For this, because 128 was contained inside 202, we will add a 1 on the binary row and we have to continue from 74 and the second decimal value 64. As you can see 64 is contained by 74 once so we will add another 1 on the binary line and we have to continue from 10. The next decimal value is 32, which is not contained inside 10 so we add a 0 on the binary line, and also because the next decimal value which is 16 is not contained inside 10, we add another 0 on the corresponding binary line for 16 decimal. Following this the next value to check if it is contained by 10 is 8, and as we see it is, we will add a 1 on the corresponding binary line. We have a rest of two. The next decimal is 4 which is not contained inside 2, this means we add a 0 on the binary line. Two more rows to have a full binary number converted from decimal. We have a rest of 2 which the next decimal value fits into perfectly, making us add a last 1 on the binary field. Because this means we have a rest of 0, because it was a perfect match, we would add more 0s if we had multiple binary cells left, but because we have one, we add just one 0. The logic behind this is that we have a rest of 0 and as you can see the next decimal value is 1 which of course is not contained inside 0, so we add the 0 on the binary line. The conversion of the decimal number 202 to binary is 11001010.

Most of the times, especially if you are heading to a career of let’s say a network professional you won’t be using such conversions in day to day work. It would take too much time to do them , even if you will become very fast and good at it. The thing is you will be tired, stressed and many others reasons might interfere in why it won’t be possible for you to actually do this, instead you will be using some sort of calculator or tool that will automatically do this for you.

However it is very good and you have no future in such a domain, if you do not understand them. Do not waste time in becoming a freak over this, you only need to understand the concept, because in those few times when no other way is possible and tools or machines are not trust worthy, you will have to do it the old style, by using your brain.

With all this being said the most important conversions you will be using are the ones I already explained, binary to decimal and decimal to binary. Knowing this will make it more easy for you with the rest of the conversions, as the best ways to do them, is by using one of these two methods.

You should know in hexadecimal, we work with letters and numbers and we have a correspondence between decimal – hex. This doesn’t mean this is how you actually calculate, but hexadecimal works with 16 characters or values, as you want to call them, the numbers from 0 to 9 and 6 letters, which are actually the rest of the values from 10 to 15 as you can see below. The Hex is the notation you will see for example a MAC written. We can have let’s say a MAC of 90-FB-A6-00-65-A3 but the details of a MAC we will learn soon, how it addresses the bits and how do we group them.

VN:F [1.9.22_1171]