Calculator of numeral systems

This online service translates the number from one notation system to another. The number can be any non-negative. The base of the notation system is from 2 to 36 inclusive.

In the form of a calculator, enter a number and specify the notation system in which it, then specify the notation system to which you want to translate the number and click "Calculate".


A notation system, or numbering, is a set of rules and signs that can be used to map (encode) any non-negative number. There are certain requirements on the number systems, among which the most important are the requirements for unambiguous coding of nonnegative numbers 0, 1,... from some finite set of the range P in a finite number of steps and the ability to perform numerically arithmetic and logical operations. In addition, the number system solves the numbering problem, that is, an effective transition from digits to numbers, which in this case must have a minimum number of digits. From the successful or unsuccessful choice of the number system depends the effectiveness of solving these problems and its use in practice.

There are the following types of number systems: positional, mixed, non-positional.

In positional notation systems, the same digit (numeric sign) in a number entry takes on different values depending on its position. Thus, the position of the figure has weight in number. In general, the weight of each position is a multiple of a natural number b, b> 1, which is called the base of the number system.

In non-position notation systems, the value indicated by a digit does not depend on its position in the number. Thus the system can impose restrictions on positions of figures, for example, that they were located in descending order, or grouped by value. However, this is not a prerequisite for understanding the numbers recorded by such systems. A typical example of a non-positioning number system is the Roman numeral system, in which the Latin letters are used as digits.

In numismatics, the decimal system, the duodecimal (duodecimal), the quaternary and the six-system are especially weighty. Information technology uses binary, decimal, octal, and hexadecimal systems.