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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

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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.