Philosophy of number systems: To convert a number from one system (decimal, binary, octal, hexadecimal) to its equivalent in one of the other, we have different types of number systems, namely 1. Deci mal sy stems 2. Bi nar y systems 3. Octal systems 4. Hex adecimal systems 1. Deci mal Number Syst em: Decimal means base 10 (the prefix dec). In any number system, given the base (often referred to as radix), the number of digits that can be used to count is fixed. For example in the base 10 number system, the digits that can be used to count are 0,1,2,3,4,5,6,7,8,9. Generalizing that for any base b, the first b digits (starting with 0) represent the digits that are used to count. When a number ≥ b has to be represented, the place values are used. Example: Consider the number 1234.567. It is represented as 1*103+ 2*102 + 3*101 + 4*100+ 5*10-1+ 6*10-2+ 7*10-3 Where: • 5 is in the tenth’s place
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