Computer Science – 13.3 Floating-point numbers, representation and manipulation | e-Consult

Normalising floating-point numbers involves adjusting the representation of a number to ensure that the mantissa (significand) has a leading '1' (except for denormalised numbers). This is achieved by shifting the binary point until only one non-zero digit is to the left of the binary point. The exponent is then adjusted accordingly to maintain the original value of the number.

Benefits of Normalisation:

• Improved Representation: Normalisation allows for a more compact and efficient representation of numbers. It avoids having many leading zeros in the mantissa, which would waste storage space.
• Increased Precision: By ensuring a consistent leading '1' in the mantissa, normalisation improves the precision of floating-point numbers. This is because it allows for a more accurate representation of numbers with varying magnitudes.
• Avoidance of Denormalisation: Normalisation helps to avoid the issue of denormalisation, where the exponent is too small to represent a significant number, leading to a loss of precision.

Implications of Exponent and Mantissa:

The exponent determines the magnitude of the number, while the mantissa determines the precision. A larger exponent represents a larger number, and a larger mantissa represents higher precision. Normalisation ensures that the relationship between the exponent and mantissa is consistent, allowing for accurate representation of numbers across a wide range of magnitudes. Incorrectly handling the exponent and mantissa can lead to significant errors in floating-point calculations.