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The TCP/IP Guide  9  Networking Fundamentals       9  Backgrounder: Data Representation and the Mathematics of Computing

Decimal, Binary, Octal and Hexadecimal Numbers 1 2 3 4 Binary, Octal and Hexadecimal Arithmetic

Humans are accustomed to dealing with decimal numbers, while computers use binary digits. Octal and hexadecimal numbers are “short forms” for binary numbers, where each hexadecimal digit takes the place of either three or four binary digits. Since people and computers speak different “number languages”, it is often necessary to convert numbers from one of these systems to the other. If you spend any amount of time dealing with computers or networks, you will find yourself needing to do this on occasion, so it's worth taking a quick look at how it is done.

First of all, let me say this: the easiest way to convert between decimal, binary, octal and hexadecimal numbers is to use a scientific calculator. This is what most people do, and I highly recommend it. However, there are cases where you may need to be able to do this by hand—we don't all always have a calculator on us. Also, understanding the manual conversion process will help you comprehend more intuitively how binary, octal and hexadecimal numbers work. So, let's take a look.

Decimal, Binary, Octal and Hexadecimal Numbers 1 2 3 4 Binary, Octal and Hexadecimal Arithmetic