When working with any kind of digital electronics in which numbers are being represented, it is important to understand the different ways numbers are represented in these systems. The number system based on ones and zeroes is called the binary system ( because there are only two possible digits ). Before discussing the binary system, a review of the decimal ( ten possible digits ) system is in order, because many of the concepts of the binary system will be easier to understand when introduced alongside their decimal counterpart. A number, whatever is the numerical system adopted, is always the same number. If you have 8 dollars in your pocket, you may say: I have 1000 dollars ( as binary ) or 10 dollars ( as octal ) or 8 dollars ( as hexadecimal ), but in your pocket you'll always find only 8 dollars ( in decimal ). Actually, you write 1000, as binary, but you read 8, in decimal. Computers only know the binary system, but when talking to humans, they try to translate the long binary numbers chains in some easier and readable numeric system: octal, hexadecimal or decimal. If the humans decide to talk to computers, they have to learn the machines own language, the binary system, and their own numbers representations. And all that is the scope of this article: Binary Representation of positive integers, Signed Binary Integers, Positive binary fractions, Signed binary fractions.

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