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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)

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