We have the following table which will help you with Hex to Binary conversion and I will also explain the concept in the next lines.
Either you learn the table and you know the conversion or you learn the logic behind it and you will know the table by understanding how the thing is actually calculated.
Logically there is no use to convert a binary or decimal form IP to a hex one. However, it might be of use to convert a MAC hex form to a binary or decimal one or backwards. Now, with the use of IPv6, the purpose of an IP being converted to or from hex becomes more logic. IPv6 is already written down in hexazecimal notation because of the agreed format. An IPv6 is formed of 8 groups of 4 hexazecimal characters separated by “:”. This means that an IPv6 address takes 128 bits. As an example of an IPv6 address we have: 4073:0100:F231:0010:0100:09D0:786B:310E.
So, as you can see, there were not many reasons in networking to find hex numbers and conversions from hex to binary or decimal, but now there might be the case as before the most commonly term that used hex was MAC address, while now we have IPv6 addresses too.
Example of Hex to Binary Conversion
So we will start with the same MAC address we used above 90-FB-A6-00-65-A3.
A MAC address has a length of 48 bits. Cisco notation and devices use mostly 3 groups of 4 chars, while rest of the sources, like Windows or people, use as they seem fit 6 groups of 2 chars but with different notations, some split them with “:”, others with ”-” and some don’t split them at all. This is how Windows also asks it when you are doing some settings with it. Why am I telling this?
48 bits split in 6 groups, meaning each group has 8 bits, each char has 4 bits. A Binary to Hex Conversion would mean each hex char will be represented on 4 binary bits according to the table. If you don’t want to remember the table, you can understand the example below. Let’s take the first group, which is 90.
If we put this into a table for better insights we will have:
This table should represent the first “9” that should be the added result of the value of the exponents. For example a binary 1010, would be 8+0+1+0, which equals 9, our first char.
You have to see each hex number as a 4 bits math sum, the lowest can be 0000 which is 0 in hex and the highest can be 1111 which is the max: 15 which is F in hex. Each of the powers added will give you the hex number but you must remember, it depends on how many groups you have and if you calculate the bits needed correctly.
The next char, the 2nd would be 0, which I already said it is the lowest and in a table would look like this:
Binary to Hex number conversion = 0.
The next group, two chars would be FB, we will calculate this in the same table:
First char I already wrote about is F and we know it’s the highest and its representation in binary on 4 bits is 1111.
The second char out of these two which is B, we know it is actually 11. So the sum of the 4 bits must be 11. You can apply the same principle of the Decimal to Binary Conversion if you want and do the division, which is so simple: 8 is contained by 11, so we have a first 1, then because the rest is 3, and the next binary value would represent 4, we will count a 0 on the binary row.
We have a rest of 3, and a 2 which is actually the next number on our table, corresponding to 21 and it’s contained inside 3, so we put a 1 on the binary field, and then the rest of 1, divided by the next binary value: 1. So we add a last 1 on the row and we have according to table below a perfect match and there is B who is actually 1011 in binary.