What representation of numbers allows for a wider range of values to be manipulated by the computer, but has relatively slower operations compared to fixed-point representation?

Floating point representation allows for a much wider range of values to be manipulated by the computer compared to fixed-point representation. This is achieved through its ability to represent very small and very large numbers efficiently by using a format that includes a significand (or mantissa) and an exponent. This capability is particularly important in scientific calculations, graphics processing, and any application that requires a high level of precision over a broad range of magnitudes.

In contrast to fixed-point representation, which has a fixed number of digits to represent values (limiting both the range and precision), floating point representation accommodates a dynamic range of values, enabling more complex and nuanced calculations. However, the trade-off lies in the processing speed; floating point operations generally require more computational resources and time, as the calculations involve more intricate procedures like normalization and potentially rounding errors.

Understanding this distinction is crucial in software design and development, especially when optimizing for performance or storage efficiency in applications requiring numerical computations.