Floating Point Number Normalisation

The process of normalisation is very useful when working with extremely large or extremely small numbers. This is because the normalised version of a fractional number provides a unique representation for a number and allows the maximum possible precision with a given number of bits. A planetary scientist dealing with huge distances or a microbiologist dealing with tiny numbers would both be in need of using the normalised form!

Teaching Presentation with demos (step by step) and exam questions

Additional Presentation

Further Explanation

Think of it as the equivalent of the standard form for denary numbers.

• The normalised version of a positive fractional number has no leading zeros after the binary point — a normalised positive number always starts as 0, point, 1,0.1
• The normalised version of a negative fractional number has no leading ones after the binary point — a normalised negative number always starts as 1, point, 0,1.0

Moreover, the mantissa of a floating point number holds the significant bits of that number, i.e. the detail of the value of a number. This means that when you need to store very precise fractional numbers, you benefit from having lots of bits after the binary point.