Understanding Binary Notation vs. Decimal Notation

Course: NETW202 - Introduction to Networking

It’s important to understand the difference between a binary number system and a decimal number system because IPv4 addresses are made up of 32-bits. Bits are written in binary but are converted into decimal notation for easier readability (Academy, C.N., 2017). No one wants to read a bunch of 0’s and 1’s.

The decimal system is a sequence of 10 digits ranging from 0 to 9. Because the decimal system is made up of a sequence of 10 numbers, its base is 10. This is important because the base number becomes your radix, or the number upon which you apply an exponent to get the positional value. The position in the decimal number sequence becomes the exponent which you use to identify the result – the positional value.

As stated in several earlier posts, binary is made up of the numbers 0 and 1. Because it is only made up of 2 numbers, its base is 2. So 2 is your radix. A bit has 8 digits of 0’s or 1’s, so the sequence position ranges from 0 to 7. This becomes your exponential value. Multiplying the radix and the exponent gives you a sequence of numbers that you can use to convert a bit into binary positional notation.

Now that you have your binary positional notation in the following sequence:

128, 64, 32, 16, 8, 4, 2, 1

To convert a decimal number such as 11000000, you place the number below your above notation, like this:

128, 64, 32, 16, 8, 4, 2, 1

 1,    1,   0,   0,  0, 0, 0, 0

Now you simply multiply the first row of numbers by the values in the second row and add the products.

So, 1 x 128 = 128, 1 x 64 = 64, 32 x 0 = 0, 16 x 0 = 0, 8 x 0 = 0, 4 x 0 = 0, 2 x 0 = 0, 1 x 0 = 0.

The sum of the results is : 128 + 64  which equals 192

This result is a binary number converted into decimal notation.

References

Academy, C. N. (2017). Introduction to Networks v6 Companion Guide, 1st Edition. [Bookshelf Online]. Retrieved from https://online.vitalsource.com/#/books/9781323805046/