Numeral system – a way of record of numbers by means of special signs, that is representation of number in writing. The numeral system gives to number a certain standard notion. Depending on an era and a scope existed and the set of numeral systems continues to exist.
Instruction
1. The existing numeral systems can be divided into three main types: position, mixed and not position.
2. In position numeral systems the sign or figure can have various value depending on a position. The system is defined by quantity of the symbols applied in it. The most popular and the decimal numeral system used everywhere. In it all numbers are presented by a certain sequence of ten figures from 0 to 9.
3. Operation of all digital equipment is based on a binary numeral system. In it only two symbols are applied: 1 and 0. All huge set of numbers are presented by various combinations of these figures.
4. At certain calculations, ternary and octal numeral systems are applied. Also so-called account for dozens or a duodecimal numeral system is known. In computer science and programming the hexadecimal numeral system as she allows to write down a machine word – unit of data when programming has great popularity.
5. The mixed numeral systems are similar to position. In the mixed systems of number are presented by the increasing sequence. The interrelation between members of this sequence can be absolutely different.
6. So, it is possible to refer the sequence of Fibonacci in which each number is equal to the sum of two previous numbers of the sequence, since 1 to the mixed numeral system. That is the sequence has an appearance 1, 1 (1+0), 2 (1+1), 3 (1+2), 5 (2+3) and so on.
7. If to represent record of time in a format day-hour-minute-second, then it is the mixed numeral system too. Any of members of the sequence can express through minimum, that is in a second. The example of the mixed system which is often used in mathematics is also the factorial numeral system presented by the sequence of factorials.
8. In not position numeral systems the value of a symbol of a system is fixed and does not depend on its situation. These systems extremely seldom are applied, besides they are difficult mathematically. Characteristic examples of such systems are: numeral system of Stern-Broko, system of residual classes, binomial numeral system.
9. At different times at the different people the set of numeral systems was applied. So, for example, great popularity the Roman numeral system known had to this day. In it for record of numbers Latin letters V — 5, by X — 10, L — 50, C — 100, D — 500, M — were used 1000.
10. Also such numeral systems as single, quinary, Babylon, Jewish, alphabetic, Ancient Egyptian, the Maya numbers, to kip, Inca were known.