The **binary calculator** allows you to convert integer and fractional numbers from one number system to another. The base of the number system cannot be less than 2 and more than 36 (10 digits and 26 Latin letters after all). The number must not exceed 30 characters. To enter fractional numbers, use the. or a symbol. To transfer a number from one system to another, enter the original number in the first field, the base of the original number system in the second and the base of the number system in which you want to convert the number in the third field, and then click the “Get Record” button.

**Number systems**

Number systems are divided into two types: positional and non-positional. We use the Arab system, it is positional, and there is also the Roman system – it is just not positional. In positional systems, the position of a digit in a number uniquely determines the value of that number. This is easy to understand by looking at the example of a number.

**Convert of numbers from one number system to another**

The easiest way to convert a number from one number system to another is to convert the number first into the decimal number system, and then, the result obtained in the desired number system.

**Convert numbers from any number system to decimal number system**

To convert a number from any number system to decimal, it is enough to number its digits, starting from zero (the digit to the left of the decimal point) similarly to examples 1 or 2. We find the sum of the products of the digits of the number on the basis of the number system in the degree of the position of this digit:

**Converting numbers from a decimal number system to another number system**

To **convert decimals to binary** numbers from the decimal number system to another number system, the integer and fractional parts of the number must be translated separately.

Convert the integer part of a number from the decimal number system to another number system

The integer part is converted from the decimal number system to another number system by sequentially dividing the integer part of the number by the base of the number system to obtain the whole remainder less than the base of the number system. The result of the transfer will be a record of balances, starting with the last.

**Convert the fractional part of a number from the decimal number system to another number system**

Recall that a regular decimal fraction is a real number with a zero-integer part. To convert such a number into a number system with base N, you need to sequentially multiply the number by N until the fractional part is reset to zero or the required number of digits is obtained. If, when multiplying, a number with an integer part other than zero is obtained, then the integer part is not taken into account further, since it is sequentially recorded in the result.

Convert the number to binary. Solution: (0 – the integer part, which will become the first digit of the result), (0 – the second digit of the result), (1 – the third digit of the result, and since the fractional part is zero, the translation is completed)