As children we learned to count using decimal, and that there are 10 decimal values: The easiest way to carry on counting after 9, is putting a one, on the left-hand side of each number. 0 becomes 10, 1 becomes 11 and so on. You then have the values: 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19. By repeating this process with the ten's column, you then have: 20, 30, 40, 50, 60, 70, 80 and of course 90. All of the numbers we can possibly think of, use a combination of those digits. A binary numbering scheme, however, only has two possible values: one or zero. Where one is referred to as ‘on’, while zero is ‘off’. 

The word binary comes from ‘Bi’ meaning two. Words like bicycle (two wheels) and binoculars (a pair of telescopes mounted side by side) are common examples. In the digital realm, computers are designed to use binary language to function. So, in order to program, you’ll need to understand how binary works. So let’s give this topic a closer look. 

You’re likely to have heard the term ‘bits’ before. For example: a 32-bit or 64-bit processor. The word ‘bit’ is short for Binary digit, meaning it’s just a single number: a one or a zero. These bits can be combined to create larger files, like bytes or megabytes… that we use to measure the size of our files. You will never convert such large files into decimal numbers; nevertheless, understanding how smaller binary numbers correspond to decimal numbers may prove to be very handy in your everyday activities. For this reason, let’s see how binary numbers correspond to decimal numbers using a table. 

Binary numbers can look odd and quite confusing, when they are written in full. This is because the digit value is increasing by the power of two, rather than what we’re used to: in decimal numbers, they  increase by powers of ten. This means that they use: 1, 2, 4, 8, 16, 32 etc. Instead of 1, 10, 100, 1000 etc. To calculate the binary value: add up all the numbers that are ‘on’ in the table. For example, the binary value of 1 0 1 0 1 0 1 is calculated as 64+16+4+1, which equals 85. Note that 32, 8 and 2 are set to zero or off, so we don’t include them in the calculation. 

Now let’s look at a more practical use of the binary code. For that, let’s take an IP address. The most common address you will encounter as a network engineer is an IPv4 address. An IPv4 address is 32 bits long. As I mentioned earlier, each binary digit is a bit. Hence, this IPv4 address is made up of 32 binary digits. This IPv4 address, with a total of 32 bits, is broken down into four equal-sized segments, then represented as decimal. This is known as ‘Dotted Decimal Notation’. For example: during a telephone conversation, we tend to repeat a phone number a couple times to double check it’s the right number. Imagine trying to tell a colleague this binary address during a telephone conversation. Chances are, you’d make a mistake. 

When we type in an IP address, the computer converts it into binary automatically. To fully understand how IP addresses work, we need to be able to do the same. So, in a table, if you split the binary value into eight-bit segments you get: 1100 0000 – 1010 1000 – 0000 0001 – 1111 1110. After you’ve done that, convert each segment to decimal. 

Now, let’s do the calculation. 128 + 64 = 192 and so on, with each segment until you get: 192.168.1.254. Using this approach, the maximum value of each of the four decimal values is 255. For example, in a class C subnet mask (which has the most significant 24 bits set to 1) the binary would look like this… In summary, Binary to decimal conversion (and vice versa) may seem difficult at first... but once you get the gist of it, you will be able to calculate these in no time... And as a Network Engineer, this will help you immensely!