The algorithm for obtaining coefficients a i becomes more obvious. With 0 в‰¤ a i < N we have a representation of M in base N system and write Representation of a number in a system with base (radix) N may only consist of digits that are smaller than N. The converter will accept this common notation which is, however, not necessary. It is customary to prefix hexadecimal numbers with 0x and octals with 0. B stands for the decimal 11 in any number system with base greater than 11, and so on. If N > 10, the missing digits come from the alphabet (usually disregarding the case.) Thus A stands for the decimal 10 in any number system with base greater than 10. For example, in the binary (N = 2) system there are only two digits: 0 and 1 in the decimal (N = 10) there are ten of them: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Please note that the number of digits in any base (also called radix) N is exactly the same number N. Input a number in any base and, to see the conversion, click on any other input control. Another device permits the user to specify the bases of conversion. The device below converts between 8 different bases. Before you smile indulgently, try multiplying or even just adding the Roman numerals CCLXIV, MDCCCIX, DCL, and MLXXXI without first translating them. The professor responded that German universities would be sufficient to teach the boy addition and subtraction but he would have to go to Italy to learn multiplication and division. A German merchant of the fifteenth century asked an eminent professor where he should send his son for a good business education.

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