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Number System: Binary, Decimal, Hexadecimal

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Binary and hexadecimal numbers are two alternatives to the traditional decimal numbers. Critical elements of computer networks like addresses, masks, and keys all involve binary or hexadecimal numbers. Understanding how such binary and hexadecimal numbers work is essential in building, troubleshooting, and programming any network.

Decimal number

The decimal number system that people use every day contains ten digits, 0 through 9. Start counting in decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, Oops! There are no more digits left. How do we continue counting with only ten digits? We add a second column of digits, worth ten times the value of the first column. Start counting again: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 (Note that the right column goes back to zero here.), 21, 22, 23, ... , 94, 95, 96, 97, 98, 99, Oops! Once again, there are no more digits left. The only way to continue counting is to add yet another column worth ten times as much as the one before. Continue counting: 100, 101, 102, ... 997, 998, 999, 1000, 1001, 1002, .... You should get the picture at this point.

Another way to make this clear is to write decimal numbers in expanded notation. 365, for example, is equal to 3×100 + 6×10 + 5×1. 1032 is equal to 1×1000 + 0×100 + 3×10 + 2×1. By writing numbers in this form, the value of each column becomes clear.

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