Floating-point and fixed-point data types are two ways of representing numerical values, each with its own characteristics and applications.

Floating-Point Data Types

Floating-point data types are designed to represent real numbers, which can vary significantly in size, including very large or very small values. The term ‘floating-point’ refers to the ability of the decimal point to “float,” meaning it can be positioned anywhere relative to the significant digits of the number. This representation involves two main components: a base number and an exponent.

For instance, the number $123.45$ can be expressed in floating-point notation as:

This format allows for a broad range of values, but it comes with a trade-off in precision. When working with floating-point numbers, rounding errors may occur, especially if the number of decimal places exceeds the precision that the data type can accommodate. To delve deeper into the underlying principles of floating-point representation, please refer to our additional resources.

Fixed-Point Data Types

In contrast, fixed-point data types are utilized to represent numbers with a predetermined number of digits both before and after the decimal point. The term ‘fixed-point’ indicates that the decimal point is in a constant position. For example, if a fixed-point data type is configured to allow two digits after the decimal point, the number $123.456$ would be represented as $123.45$, which entails rounding off the last digit.

Fixed-point numbers offer greater precision compared to floating-point numbers but are limited in range. They are particularly useful in financial calculations, where maintaining accuracy is often more critical than accommodating a wide range of values. For a more comprehensive understanding of different data types, please consult our notes on the subject.