Components of electronic machines, which include computers, have only two distinguishable states: there is current and no current.
They are designated "1" and "0" respectively.
Since there are only two such states, many processes and operations in electronics can be described using binary numbers.
In order to translate a fractional decimalNumber in the binary system, use the following algorithm. Consider the operation of the algorithm on the example of the number 235.62. First, the integer part of the number is translated.
Divide the decimal number by two untilWe obtain an indivisible residue. At each division step, we get the remainder 1 (if the dividend number is odd) or 0 (if the dividend is divisible by two without remainder). All these residues must be taken into account. The last partial result, obtained as a result of such a step division, will always be a unit.
We write the last unit in the highest orderOf the desired binary number, and the residuals obtained in the process are written down for this unit in the reverse order. Here you have to be careful not to miss zeros.
Thus, the number 235 in the binary code will correspond to the number 11101011.
Now we translate it into a binary number systemThe fractional part of the decimal number. To do this, we multiply the fractional part of the number by 2 and fix the integer parts of the numbers obtained. These integer parts are added to the number obtained in the previous step after the binary point in the direct order.
Then the decimal fractional number 235.62 corresponds to the binary fractional 11101011.100111.