Introduction
In this article, we discuss What is Binary Fractions and its applications, Binary fractions are a way of representing fractional numbers in binary form. They are used in digital systems, such as microcontrollers and computer processors, for processing fractional values.
Characteristics
In binary fractions, each bit represents a fraction of a power of 2, with the least significant bit representing 1/2, the next bit representing 1/4, and so on.
Construction
To represent a binary fraction, the fractional value is multiplied by 2 and the integer part is written down as a binary digit. This process is repeated with the fractional part of the result until the desired precision is reached.
Working: Binary fractions can be added, subtracted, multiplied, and divided using similar rules as for integer binary numbers. However, special care must be taken to ensure that the precision of the result is maintained.
Procedure
To add or subtract binary fractions, they must first be aligned so that the decimal points are in the same position. and To multiply binary fractions, the fractional parts are multiplied as usual, and the final result is shifted to the right by the number of bits representing the fractional part. To divide binary fractions, the fractional part of the divisor is inverted and multiplied with the dividend.
Rules
The precision of the result must be maintained throughout any arithmetic operation with binary fractions. Overflow and underflow must also be considered, as the number of bits used to represent the fractional part is limited.
Formula
To convert a binary fraction to a decimal fraction, each bit representing a power of 2 is multiplied by the corresponding fractional value and the results are added together.
Need
Binary fractions are needed in digital systems for representing fractional values in a compact and efficient manner. In digital systems, all data is represented in binary form using only 1s and 0s. Binary fractions allow for the representation of fractional values using a similar format, without the need for a separate notation.
Some specific needs for binary fractions are:
- Efficient storage: Binary fractions take up less memory than other forms of fractional notation, such as decimal fractions, making them ideal for storage in digital systems with limited memory.
- Efficient processing: Binary fractions can be processed using similar rules as for integer binary numbers, allowing for efficient processing in digital systems.
- Precision: Binary fractions allow for a high level of precision in representing fractional values, with each bit representing a fraction of a power of 2.
- Compatibility: Binary fractions are compatible with the binary format used in digital systems, making them easy to work with and integrate into digital systems.
- Accuracy: Binary fractions can accurately represent any rational number, providing accurate results in calculations involving fractional values.
Applications
The applications for of Binary Fractions and its applications
- Microcontrollers
- Computer processors
- Digital signal processing
- Audio and video processing
- Image processing
- Control systems
- Communications systems.