The numeral system is a method of representation of numbers in mathematics. For record a certain set of character, figures and/or Latin letters is used. To transfer any number to a decimal system, it is necessary to transform it by certain rules.
Instruction
1. The value of decimal number depends on arrangement of its figures. This way of record is called a position system. Such systems a set, it is possible to take for the basis not only 10. For example, octal and hexadecimal systems and also binary which computers for transfer use, storages and codings of data are quite widespread. The binary code of number represents various combinations only of two symbols: 0 and 1. Despite convenience of application by computers, such system is difficult perceived by the person.
2. Number in a position numeral system it is possible to present the sums of elements in the form. These elements are works of figures of number on the basis built in the corresponding degree. Categories of numbers go on decrease, therefore, to begin more conveniently on the right, i.e. with zero degree. For example, binary number 011101 is equal 1•2^0 + 0•2 ¹ + 1•2² + 1•2³ + 1•2^4 + 0•2^5 = 29.
3. Thus, it is possible to transfer any number to a decimal system. Try to transform septenary number 743: 743_7 = 3 · 7^0 + 4•7 ¹ + 7•7² = 374_10. At first sight, the situation when the basis more than 10, but it not so looks a little difficult. In this case it is just necessary to remember that when figures come to an end, the Latin alphabet is used. In relation to hexadecimal record it means that capital letters of A = 10, B = 11, C = 12, D = 13, E = 14, F = 15 participate in it. Example: 12FE_16 = 14•16^0 + 15•16 ¹ + 2•16² + 1•16³ = 4849.
4. Besides position numeral systems exist also not position when the symbol position in number does not influence its general meaning. A striking example of such record is Roman. In it a limited set of capital Latin letters is used: I, V, H, L, S, D and M. For transfer of such numbers to a decimal look it is necessary to know values of these symbols: I = 1; V = 5; Х = 10; L = 50; With = 100; D = 500; M = 1000
5. Besides, there are two basic principles. The principle of addition is that if the big figure takes a position before smaller, then they develop. In the return case – smaller it is subtracted from bigger: MCMLXXXI = 1 + 10 + 10 + 10 + 50 + 900[CM=1000–100] + 1000 = 1981; MMXII = 2 + 10 + 1000 + 1000 = 2012.