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Binary-to-Decimal Conversion

To understand the operation of a device in a network, you need to look at addresses and other data the way a network device does: in binary notation. This means that you need to have some skill in binary-to-decimal conversion.

Data represented in binary can represent many different forms of data to the human net-work. In this discussion, binary is discussed as it relates to IPv4 addressing. This means that each byte (octet) is interpreted as a decimal number in the range of 0 to 255.

Positional Notation

Learning to convert binary to decimal requires an understanding of the mathematical basis of a numbering system called positional notation. Positional notation means that a digit

represents different values depending on the position it occupies. More specifically, the value that a digit represents is the value of the digit multiplied by the power of the base, or radix, represented by the position the digit occupies. Some examples will help to clarify how this system works.

For the decimal number 245, the 2 is in the 100s, or 10², position. Therefore, this 2 repre-sents 2*10² (2 times 10 to the power of 2). Positional notation refers to this position as the base² position because the base, or radix, is 10 and the power is 2.

Using positional notation in the base 10 number system, 245 represents the following:

245 = (2 * 10²) + (4 * 10¹) + (5 * 10⁰)

or

245 = (2 * 100) + (4 * 10) + (5 * 1)