Normalisation of floating-point numbers can lead to information loss, particularly in terms of precision. This loss occurs because the normalisation process involves shifting the mantissa to fit a certain format. When the mantissa is shifted, the least significant bits may be discarded if they extend beyond the mantissa's capacity. For instance, if a binary floating-point number has more bits than the mantissa can hold, normalising it will result in the excess bits being lost. This loss is particularly impactful when dealing with very small or very precise numbers, as the discarded bits could represent important information about the number's precision. While normalisation is essential for standardising the representation of floating-point numbers and maximising the use of the mantissa, it is a trade-off between precision and a uniform, efficient representation.

Handling zero in floating-point arithmetic during normalisation poses a unique challenge because zero cannot be normalised in the traditional sense. In a normalised floating-point number, the leading digit of the mantissa is non-zero. However, zero has no non-zero digits, making it impossible to follow the standard normalisation process. To address this, floating-point systems typically have a special representation for zero. This representation often involves setting all bits of the mantissa to zero and may also involve a specific exponent value, depending on the floating-point standard used (like IEEE 754). This special case handling is crucial because it ensures that zero, an important value in arithmetic, can be represented accurately and consistently in floating-point systems, while also distinguishing it from very small non-zero numbers.

Normalisation of floating-point numbers is particularly important in computing situations that require high precision and accuracy, such as scientific computations, engineering simulations, and financial calculations. In these fields, the accuracy of numerical data is paramount, and normalisation ensures that the floating-point numbers used in calculations are as precise as possible. It also plays a critical role in algorithms that compare floating-point numbers. Normalised numbers have a consistent format, making comparison operations more straightforward and reliable. Furthermore, in graphics and visualisation tasks, normalisation helps maintain accuracy in colour representations and spatial calculations. Additionally, in domains where data is transmitted or stored, normalisation ensures that floating-point numbers occupy a uniform amount of space, enhancing data compression and transmission efficiency.

The normalisation of floating-point numbers, while beneficial for standardisation and precision, comes with certain limitations. One significant limitation is the inability to represent very small numbers accurately. In cases where a number is extremely close to zero but not exactly zero, normalisation may lead to a loss of precision. This is because, in the effort to normalise the number, significant digits might be lost or shifted out of the mantissa's range. Another limitation is the additional computational overhead. Normalising a number requires processing power to shift the mantissa and adjust the exponent, which can be resource-intensive in systems where performance is a critical factor. Additionally, normalisation does not entirely eliminate rounding errors; it only minimises them. In certain calculations, especially those involving a large number of floating-point operations, these rounding errors can accumulate, leading to less accurate results.

In binary systems, normalisation of floating-point numbers typically involves adjusting the number so that the first digit to the left of the binary point is a '1'. This is because binary numbers only have '1' and '0', and having the first digit as '1' maximises the precision. In contrast, decimal floating-point normalisation involves adjusting the number so that the first digit to the left of the decimal point is not zero, and it can range from 1 to 9. This is because decimal numbers have ten possible digits (0-9), and placing any non-zero digit in the highest place value ensures maximum precision. The process is fundamentally the same in both systems: shifting the mantissa and adjusting the exponent accordingly. However, the base of the numeral system dictates the specific digit that should lead the mantissa.