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How to translate into binary system

only two digits used in the binary system: zero and one

In the components of electronic machines, which include computers, there are only two distinct states: there are no current and voltage.

They represent a "1" and "0" respectively.

As such, only two states, many of the processes and operations in electronics can be described by binary numbers.



To convert a decimal fractionnumber in the binary system, proceed according to the following algorithm. Consider the action of the algorithm on an example of the number of 235.62. First, it translates the integer part of.


Decimal divide into two as long as noWe get two indivisible remainder. At each step, we get the rest of the division 1 (if the dividend is an odd number) or 0 (if the dividend is divided by two without a remainder). All these residues have to be taken into account. Last quotient obtained by dividing this step, will always be one.
Write the last unit in the MSBSeeking a binary number, and the remainder received in the record for this unit in the reverse order. Here we must be careful not to miss the zeros.
Thus, the number 235 in binary code corresponds to the number 11101011.

Divide the original number by 2 (the base of the binary system)


Now converted into a binary number systemthe fractional part of a decimal number. For this series we multiply the fractional part of the number 2, and fix the whole of the numbers obtained. These integral part appends to that obtained in the previous step to the number of the binary point in a direct manner.
Then decimal fractional number 235.62 corresponds to the binary fraction 11101011.100111.

Multiply the fractional part 2, until we reach the desired accuracy of

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