Binary Number System: Numbers with a Fractional Part

Fractional binary numbers represent values that exist between whole numbers. They’re similar to decimal fractions but use a binary number system instead.
A binary fraction is placed to the right of the binary point. For example, in the binary number ‘101.01’, ‘.01’ is the fractional part.
Each binary fraction represents a ‘portion’ of 2, such as 1/2 (0.5 in decimal) for the first digit after the binary point, 1/4 (0.25 in decimal) for the second digit, and so on.

Converting a fractional binary number to a decimal involves multiplying each digit after the point by 2 raised to the negative power of its position. For instance, in ‘.101’, the first ‘1’ is multiplied by 2^(-1), and the second ‘0’ by 2^(-2).
The sum of these calculations provides the decimal equivalent of the fractional binary number.

To convert a decimal fraction to binary, multiply the fraction by 2 and record the integer part. Repeat the process with the remaining fractional part until it becomes zero or until a desirable level of precision is reached.
The binary representation is then composed of the integer parts obtained in each step, from top to bottom.

Fractional binary numbers have a critical role in computing and digital systems. They enable the representation and operations of non-integer values in binary form.
Common applications include graphics programming, digital signal processing, and scientific computations where precision and fractional values are frequently used.
It is crucial to consider the precision while dealing with fractional binary numbers as binary fractions may not accurately represent all decimal fractions, which can lead to rounding errors.