# How to Convert of Numbers Into Various Number Systems

|Convert of numbers into various number systems

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 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 toconvert 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 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)