In a more general sense, binary systems can be anything which offers only two options, not necessarily limited to numerical systems. Mathematical methods exist for transforming binary numbers into decimal numbers, and visa-versa. If you have say a decimal number of 254, to work out the binary code you would use the system above to work it out.
While the most common counting system, the decimal system, uses ten numerals, binary uses only 0 and 1. There are also mathematical devices for performing functions such as addition, subtraction, multiplication and division in different base-systems, including binary. Several of the posts show how to convert binary numbers (up to eight columns in length) to a base-10 number.To count in binary means you only have two numbers, 0 and 1! While conversion to or from decimal is somewhat labored, converting between binary and octal or hexadecimal systems, base-eight and base-16 respectively, is much easier. I suggest you make sure you understand binary code first before moving onto hex because the development between them can become very confusing.
This is because both eight and 16 are powers of two, making them integrate well with binary systems.
It is for this reason that both octal and hexadecimal are widely used base-systems in computer applications.
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